A354550 Expansion of e.g.f. exp( x * exp(x^2/2) ).

1, 1, 1, 4, 13, 46, 241, 1156, 6889, 44668, 300241, 2328976, 18390901, 159273544, 1461200833, 13995753136, 144068872081, 1531949061136, 17259159775969, 202543867724608, 2474236899786781, 31633380519660256, 417760492214548561, 5751414293905728064

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..518

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(2^k * k! * (n - 2*k)!).

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[x Exp[x^2/2]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 03 2024 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^2/2)))))
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(2^k*k!*(n-2*k)!));

Crossrefs

Cf. A000248, A354551, A354552.

Cf. A216688.

Sequence in context: A218667 A149439 A014145 * A143566 A098841 A363547

Adjacent sequences: A354547 A354548 A354549 * A354551 A354552 A354553

Keyword

nonn

Author

Seiichi Manyama, Aug 18 2022

Status

approved