A316986 E.g.f. A(x) satisfies: Sum_{n>=0} 1/n! * exp(n^3*x)/A(x)^n = exp(1).

1, 5, 128, 11392, 2236652, 759228380, 392139771304, 285703074106040, 279350809692772496, 353786526283994569936, 565007365484930130348992, 1114018384038502393664134976, 2665220313156774054232566020416, 7625388922708469482877177712163904, 25767788855967203399405930764145179520, 101739876623828618561739304251029747402368

Offset

0,2

Links

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

Example

E.g.f.: A(x) = 1 + 5*x + 128*x^2/2! + 11392*x^3/3! + 2236652*x^4/4! + 759228380*x^5/5! + 392139771304*x^6/6! + 285703074106040*x^7/7! + 279350809692772496*x^8/8! + ...
such that
e = 1 + exp(x)/A(x) + exp(8*x)/A(x)^2/2! + exp(27*x)/A(x)^3/3! + exp(64*x)/A(x)^4/4! + exp(125*x)/A(x)^5/5! + exp(216*x)/A(x)^6/6! + ... + exp(n^3*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^3*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. A316567.

Sequence in context: A208859 A229147 A224250 * A355085 A316392 A277259

Adjacent sequences: A316983 A316984 A316985 * A316987 A316988 A316989

Keyword

nonn

Author

Paul D. Hanna, Jul 18 2018

Status

approved