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A376345
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x^2) - 1)) ).
3
1, 0, 0, 6, 0, 60, 2880, 840, 201600, 7998480, 12700800, 1816547040, 67898476800, 311359688640, 35628798965760, 1317155266627200, 12924530383564800, 1308998905659244800, 49463008450023168000, 863080350836537433600, 81264621182097120768000, 3227330594664084337228800, 87828327888763088096870400
OFFSET
0,4
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (2*n-2*k)! * Stirling2(k,n-2*k)/k!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x^2)-1)))/x))
(PARI) a(n) = sum(k=0, n\2, (2*n-2*k)!*stirling(k, n-2*k, 2)/k!)/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 21 2024
STATUS
approved