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
Programs
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Mathematica
With[{nn=20},CoefficientList[Series[(3-2Exp[x])^(3/2),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 19 2025 *) -
PARI
a(n) = sum(k=0, n, prod(j=0, k-1, 2*j-3)*stirling(n, k, 2));
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