A325215 G.f. A(x) satisfies: 1 = Sum_{n>=0} (1 + x)^(n^4) / A(x)^(n^2) * 1/2^(n+1).

1, 25, 60060, 1132905020, 58664467783190, 6255154686240956814, 1192613188256914797257960, 371053134042859561147801435880, 176215970882772340084884112291790190, 121357690241973072743173180485320899071350, 116393177524110499499383856118207410661782097788, 150467277168909239442664595062252878406778102486407260, 255237617230545143251655215904006414174410609980605014003290

Offset

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..50

Example

G.f.: A(x) = 1 + 25*x + 60060*x^2 + 1132905020*x^3 + 58664467783190*x^4 + 6255154686240956814*x^5 + 1192613188256914797257960*x^6 + ...
such that
1 = 1/2 + (1+x)/A(x)*1/2^2 + (1+x)^16/A(x)^4*1/2^3 + (1+x)^81/A(x)^9*1/2^4 + (1+x)^256/A(x)^16*1/2^5 + (1+x)^625/A(x)^25*1/2^6 + (1+x)^2401/A(x)^49*1/2^8 + ...

Prog

(PARI) /* Requires suitable precision */
{a(n) = my(A=[1]); for(i=0, n,
A=concat(A, 0); A[#A] = round( polcoeff( sum(n=0, 30*#A+100, (1+x +x*O(x^#A))^(n^4) / Ser(A)^(n^2) * 1/2^(n+1)*1.), #A-1))/3; ); A[n+1]}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Sequence in context: A203543 A337727 A034711 * A076445 A013835 A211600

Adjacent sequences: A325212 A325213 A325214 * A325216 A325217 A325218

Keyword

nonn

Author

Paul D. Hanna, Apr 19 2019

Status

approved