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URL: https://oeis.org/A370985

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A370985
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^3*exp(x)) ).
4
1, 0, 0, 6, 24, 60, 3000, 45570, 403536, 10644984, 297562320, 5517833310, 142801022760, 5076208052916, 150282366476424, 4713707747551530, 189345734667052320, 7517503455423740400, 295622259241028433696, 13370535071068474177974, 642403497550155241197240
OFFSET
0,4
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} k^(n-3*k) * (n+k)!/(k! * (n-3*k)!).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^3*exp(x)))/x))
(PARI) a(n) = sum(k=0, n\3, k^(n-3*k)*(n+k)!/(k!*(n-3*k)!))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 06 2024
STATUS
approved