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A376351
E.g.f. satisfies A(x) = exp( x*A(x)*(exp(x^2*A(x)^2) - 1) ).
0
1, 0, 0, 6, 0, 60, 2520, 840, 181440, 6063120, 11642400, 1437337440, 44626982400, 254278664640, 24575197046400, 756010400745600, 9284429893939200, 784770965801222400, 25067890370095372800, 541810656586725926400, 42351473267452597248000, 1461224653966598493772800, 48020130717168717960652800
OFFSET
0,4
FORMULA
E.g.f.: (1/x) * Series_Reversion( x*exp(x*(1 - exp(x^2))) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (n+1)^(n-2*k-1) * Stirling2(k,n-2*k)/k!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*exp(x*(1-exp(x^2))))/x))
(PARI) a(n) = n!*sum(k=0, n\2, (n+1)^(n-2*k-1)*stirling(k, n-2*k, 2)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 21 2024
STATUS
approved