A375651 Expansion of e.g.f. exp(x + x^2 * exp(x)).

1, 1, 3, 13, 61, 341, 2221, 16045, 127065, 1097353, 10231561, 102133241, 1085537509, 12228389629, 145369356861, 1816987580101, 23804010114481, 325966118893457, 4654236956576977, 69138950655122929, 1066449047096819901, 17050138691821539781

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(n-2*k) / (k! * (n-2*k)!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x+x^2*exp(x))))
(PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(n-2*k)/(k!*(n-2*k)!));

Crossrefs

Cf. A216507, A375652.

Sequence in context: A367059 A243014 A258799 * A246689 A355987 A373683

Adjacent sequences: A375648 A375649 A375650 * A375652 A375653 A375654

Keyword

nonn

Author

Seiichi Manyama, Aug 22 2024

Status

approved