A316567 E.g.f. A(x) satisfies: Sum_{n>=0} 1/n! * exp(n^2*x)/A(x)^n = exp(1).

1, 2, 7, 48, 613, 12678, 376635, 14843748, 736850985, 44460709034, 3178138510415, 263969177593784, 25092912792070221, 2697122248172619374, 324551651315721416259, 43360400395276940296748, 6386567528761097854601681, 1030796192558122817118624722, 181349613039877947587685266455, 34616458231107257107670541291456

Offset

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..70

Example

E.g.f.: A(x) = 1 + 2*x + 7*x^2/2! + 48*x^3/3! + 613*x^4/4! + 12678*x^5/5! + 376635*x^6/6! + 14843748*x^7/7! + 736850985*x^8/8! + 44460709034*x^9/9! + 3178138510415*x^10/10! + ...
such that
e = 1 + exp(x)/A(x) + exp(4*x)/A(x)^2/2! + exp(9*x)/A(x)^3/3! + exp(16*x)/A(x)^4/4! + exp(25*x)/A(x)^5/5! + exp(36*x)/A(x)^6/6! + ... + exp(n^2*x)/A(x)^n/n! + ...

Prog

(PARI) /* Requires setting appropriate precision and index ranges */
{a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = round( (#A-1)!*Vec( sum(n=0, 400, exp(n^2*x +x*O(x^#A) )/n!/Ser(A)^n*1. )/exp(1) )[#A])/(#A-1)! ); n!*A[n+1]}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A316986.

Sequence in context: A277501 A277503 A317666 * A304968 A281263 A206153

Adjacent sequences: A316564 A316565 A316566 * A316568 A316569 A316570

Keyword

nonn

Author

Paul D. Hanna, Jul 06 2018

Status

approved