A303289 E.g.f. A(x) satisfies: e = Sum_{n>=0} (1/n!) * (1+x)^(n^2) / A(x)^n.

1, 2, 5, 31, 390, 7926, 229448, 8769552, 421254088, 24578690456, 1699003652752, 136526757080176, 12565047627623648, 1308650039442105504, 152723805589647826368, 19806995417441865105472, 2834647872410303847945600, 444947841160313990957842304, 76198407065481146373641422336, 14170329519388795065500512696832

Offset: 0

Author

Paul D. Hanna, Apr 23 2018

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + 2*x + 5*x^2/2! + 31*x^3/3! + 390*x^4/4! + 7926*x^5/5! + 229448*x^6/6! + 8769552*x^7/7! + 421254088*x^8/8! + 24578690456*x^9/9! + 1699003652752*x^10/10! + ...
such that A = A(x) satisfies:
e = 1 + (1+x)/A + (1+x)^4/(2!*A^2) + (1+x)^9/(3!*A^3) + (1+x)^16/(4!*A^4) + (1+x)^25/(5!*A^5) + (1+x)^36/(6!*A^6) + (1+x)^49/(7!*A^7) + ...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..171

Crossrefs

Cf. A303290, A303291, A303292.

Programs

PARI

\p100; N=20;
A=[1]; for(i=1,N, A=concat(A,0); A[#A] = Vec( round( sum(n=0,200 + 2*#A, (1+x +x*O(x^#A))^(n^2)/Ser(A)^n/n!*1. )/exp(1)*(#A-1)! ) )[#A]/(#A-1)! ); Vec(serlaplace(Ser(A)))