A375991 Expansion of e.g.f. (3 - 2 * exp(x))^(3/2).

1, -3, 0, 9, 45, 252, 1935, 19989, 260190, 4063887, 73823445, 1527002694, 35408499885, 909389617497, 25618701424680, 785355764569749, 26024092206299505, 926859918577582332, 35306305954587340515, 1432301360556686816529, 61649353087003554947550

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (2*j-3)) * Stirling2(n,k).

a(n) ~ 3^(5/2) * n^(n-2) / (2^(3/2) * exp(n) * log(3/2)^(n - 3/2)). - Vaclav Kotesovec, May 20 2025

Mathematica

With[{nn=20}, CoefficientList[Series[(3-2Exp[x])^(3/2), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 19 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 2*j-3)*stirling(n, k, 2));

Crossrefs

Cf. A004123, A305404, A367470, A375948, A375954.

Cf. A006681.

Sequence in context: A336710 A294106 A377268 * A094472 A347999 A028850

Adjacent sequences: A375988 A375989 A375990 * A375992 A375993 A375994

Keyword

sign,easy

Author

Seiichi Manyama, Sep 05 2024

Status

approved