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A354392
Expansion of e.g.f. 1/(1 + (exp(x) - 1)^3 / 6).
4
1, 0, 0, -1, -6, -25, -70, 119, 4354, 48215, 371610, 1620839, -10665886, -388969945, -6114636710, -65181228841, -325375497726, 5950049261495, 226564100074970, 4447402833379079, 57902620204276834, 258292327155958535, -12701483290229413350
OFFSET
0,5
FORMULA
a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n,k) * Stirling2(k,3) * a(n-k).
a(n) = Sum_{k=0..floor(n/3)} (3*k)! * Stirling2(n,3*k)/(-6)^k.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+(exp(x)-1)^3/6)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, binomial(i, j)*stirling(j, 3, 2)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\3, (3*k)!*stirling(n, 3*k, 2)/(-6)^k);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, May 25 2022
STATUS
approved