A321607 G.f.: A(x) = Sum_{n>=0} x^n * (1+x)^(2*n^2) / A(x)^(2*n).

1, 1, 1, 3, 11, 50, 294, 1833, 13093, 100456, 830541, 7313419, 68137388, 668327844, 6873073257, 73853969234, 826869429175, 9622413867975, 116144019094407, 1451337070767512, 18744666092043742, 249848115448337748, 3432213607060089249, 48532637291552045262, 705602120522021975822, 10536473807470843781980, 161442021516682347676435

Offset: 0

Author

Paul D. Hanna, Nov 23 2018

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 11*x^4 + 50*x^5 + 294*x^6 + 1833*x^7 + 13093*x^8 + 100456*x^9 + 830541*x^10 + 7313419*x^11 + 68137388*x^12 + ...
such that
A(x) = 1 + x*(1+x)^2/A(x)^2 + x^2*(1+x)^8/A(x)^4 + x^3*(1+x)^18/A(x)^6 + x^4*(1+x)^32/A(x)^8 + x^5*(1+x)^50/A(x)^10 + x^6*(1+x)^72/A(x)^12 + ...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A303058, A321608.

Programs

PARI

{a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); A[#A] = Vec(sum(n=0, #A, ((1+x)^n +x*O(x^#A))^(2*n) * x^n/Ser(A)^(2*n+1) ) )[#A] ); A[n+1]}
for(n=0, 30, print1(a(n), ", "))