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URL: https://oeis.org/A371019

⇱ A371019 - OEIS

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A371019
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x^3*exp(x)) ).
6
1, 0, 0, 6, 24, 60, 2280, 35490, 322896, 6532344, 175392720, 3351681630, 74021715240, 2328376978356, 68824597123464, 1989994550546730, 69687384248405280, 2634948077918611440, 98220733842576688416, 3966108617957749165494, 175679596523004500742840
OFFSET
0,4
FORMULA
a(n) = (n!/(n+1)) * Sum_{k=0..floor(n/3)} k^(n-3*k) * binomial(n+1,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) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n+1, k)/(n-3*k)!)/(n+1);
CROSSREFS
Cf. A365287.
Sequence in context: A390648 A371046 A390649 * A370985 A101854 A273358
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 08 2024
STATUS
approved