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A353894
Expansion of e.g.f. exp( (x * (exp(x) - 1))^2 / 4 ).
3
1, 0, 0, 0, 6, 30, 105, 315, 2128, 24948, 251415, 2093025, 16437036, 148728294, 1693067467, 21459867975, 270217289280, 3338860150488, 42428729660751, 581966068060485, 8654787480759700, 135253842794286930, 2163416823356628147, 35313421249845594075
OFFSET
0,5
FORMULA
a(n) = n! * Sum_{k=0..floor(n/4)} (2*k)! * Stirling2(n-2*k,2*k)/(4^k * k! * (n-2*k)!).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*(exp(x)-1))^2/4)))
(PARI) a(n) = n!*sum(k=0, n\4, (2*k)!*stirling(n-2*k, 2*k, 2)/(4^k*k!*(n-2*k)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 09 2022
STATUS
approved