In[]:=
S18[n_]:=
1
a1
(a10
18n-18
2
+a9
16n-16
2
+a8
14n-14
2
+a7
12n-12
2
+a6
10n-10
2
+a5
8n-8
2
+a4
6n-6
2
+a3
4n-4
2
+a2
2n-2
2
)
In[]:=
NSolve[S18[2]==512&&S18[3]==32276480&&S18[4]==5967012429824&&S18[5]==1434047386279215104&&S18[6]==367859068909182204772352&&S18[7]==95910600411254377903510519808&&S18[8]==25108333074341105474794741072658432&&S18[9]==6579768945390796136704466286370881536000&&S18[10]==1724700842014699584005152525604862865902141440,S18[11]==452110402686837008940790840661958866701897063989248,{a1,a2,a3,a4,a5,a6,a7,a8,a9,a10},Integers]
NSolve
:
1532495540865888858358347027150309183618739122183602176a10+1048576a2+5+1393796574908163946345982392040522594123776a8+1461501637330902918203684832716283019655932542976a9
a1
452110402686837008940790840661958866701897063989248 is not a valid variable.
Out[]=
NSolve
262144a10+4a2+16a3+64a4+256a5+1024a6+4096a7+16384a8+65536a9
a1
512&&
68719476736a10+16a2+256a3+4096a4+65536a5+1048576a6+16777216a7+268435456a8+4294967296a9
a1
32276480&&
1
a1
(18014398509481984a10+64a2+4096a3+262144a4+16777216a5+1073741824a6+68719476736a7+4398046511104a8+281474976710656a9)5967012429824&&
1
a1
(4722366482869645213696a10+256a2+65536a3+16777216a4+4294967296a5+1099511627776a6+281474976710656a7+72057594037927936a8+18446744073709551616a9)1434047386279215104&&
1
a1
(1237940039285380274899124224a10+1024a2+1048576a3+1073741824a4+1099511627776a5+1125899906842624a6+1152921504606846976a7+1180591620717411303424a8+1208925819614629174706176a9)367859068909182204772352&&
1
a1
(324518553658426726783156020576256a10+4096a2+16777216a3+68719476736a4+281474976710656a5+1152921504606846976a6+4722366482869645213696a7+19342813113834066795298816a8+79228162514264337593543950336a9)95910600411254377903510519808&&
1
a1
(85070591730234615865843651857942052864a10+16384a2+268435456a3+4398046511104a4+72057594037927936a5+1180591620717411303424a6+19342813113834066795298816a7+316912650057057350374175801344a8+5192296858534827628530496329220096a9)25108333074341105474794741072658432&&
1
a1
(22300745198530623141535718272648361505980416a10+65536a2+4294967296a3+281474976710656a4+18446744073709551616a5+1208925819614629174706176a6+79228162514264337593543950336a7+5192296858534827628530496329220096a8+340282366920938463463374607431768211456a9)6579768945390796136704466286370881536000&&
1
a1
(5846006549323611672814739330865132078623730171904a10+262144a2+68719476736a3+18014398509481984a4+4722366482869645213696a5+1237940039285380274899124224a6+324518553658426726783156020576256a7+85070591730234615865843651857942052864a8+22300745198530623141535718272648361505980416a9)1724700842014699584005152525604862865902141440,
1
a1
(1532495540865888858358347027150309183618739122183602176a10+1048576a2+1099511627776a3+1152921504606846976a4+1208925819614629174706176a5+1267650600228229401496703205376a6+1329227995784915872903807060280344576a7+1393796574908163946345982392040522594123776a8+1461501637330902918203684832716283019655932542976a9)452110402686837008940790840661958866701897063989248,{a1,a2,a3,a4,a5,a6,a7,a8,a9,a10},