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A375591
Expansion of e.g.f. exp( x * (exp(x^2/2) - 1) ).
1
1, 0, 0, 3, 0, 15, 90, 105, 2520, 8505, 66150, 634095, 3118500, 40675635, 285675390, 2896618725, 31556725200, 281774718225, 3691224687150, 37783760189175, 483465043561500, 6108282465360075, 76126660317858150, 1102221773079151725, 14598579860502838200
OFFSET
0,4
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} Stirling2(k,n-2*k)/(2^k*k!).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^2/2)-1))))
(PARI) a(n) = n!*sum(k=0, n\2, stirling(k, n-2*k, 2)/(2^k*k!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 19 2024
STATUS
approved