A375807 Expansion of e.g.f. 1/(1 + (log(1 - x^2))/x)^3.
1, 3, 12, 69, 504, 4440, 45720, 538020, 7116480, 104455008, 1684005120, 29571696000, 561695238720, 11472451848000, 250694772007680, 5835284153899200, 144124039400140800, 3764378233282867200, 103661897106414366720, 3001493647870874956800
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^2)/x)^3)) -
PARI
a(n) = n!*sum(k=0, n\2, (n-2*k+2)!*abs(stirling(n-k, n-2*k, 1))/(n-k)!)/2;
Formula
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375798.
a(n) = (n!/2) * Sum_{k=0..floor(n/2)} (n-2*k+2)! * |Stirling1(n-k,n-2*k)|/(n-k)!.