A362355 a(n) = 4*(n+4)^(n-1).

1, 4, 24, 196, 2048, 26244, 400000, 7086244, 143327232, 3262922884, 82644187136, 2306601562500, 70368744177664, 2330488948919044, 83291859462684672, 3196026743131536484, 131072000000000000000, 5722274760967941313284, 264999811677837732610048

Offset

0,2

Comments

This gives the fourth exponential (also called binomial) convolution of {A000272(n+1)} = {A232006(n+1, 1)}, for n >= 0, with e.g.f. (LambertW(-x),(-x)) (LambertW is the principal branch of the Lambert W-function).

This is also the row polynomial P(n, x) of the unsigned triangle A137452, evaluated at x = 4.

Links

Table of n, a(n) for n=0..18.

Eric Weisstein's World of Mathematics, Lambert W-function

Wikipedia, Lambert W function

Formula

a(n) = Sum_{k=0..n} |A137452(n, k)|*4^k = Sum_{k=0..n} binomial(n-1, k-1)*n^(n-k)*4^k, with the n = 0 term equal to 1 (not 0)).

E.g.f.: (LambertW(-x)/(-x))^4.

Crossrefs

Column k = 4 of A232006.

Cf. A000272, A137452.

Sequence in context: A291819 A101370 A201338 * A099021 A220690 A136229

Adjacent sequences: A362352 A362353 A362354 * A362356 A362357 A362358

Keyword

nonn,easy

Author

Wolfdieter Lang, Apr 24 2023

Status

approved