A375715 Expansion of e.g.f. 1 / sqrt(1 - x^2 * (exp(x) - 1)).
1, 0, 0, 3, 6, 10, 285, 1911, 8848, 147456, 1818225, 15966775, 244374636, 4105980528, 55574016589, 938220142965, 18765940185840, 342231152117536, 6765035069902833, 154060159512672315, 3469311695227952260, 80672955862303202160, 2068943441492081794101
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-x^2*(exp(x)-1)))) -
PARI
a001147(n) = prod(k=0, n-1, 2*k+1); a(n) = n!*sum(k=0, n\3, a001147(k)*stirling(n-2*k, k, 2)/(2^k*(n-2*k)!));
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} A001147(k) * Stirling2(n-2*k,k)/(2^k*(n-2*k)!).