A370987 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^3/6*exp(x)) ).

1, 0, 0, 1, 4, 10, 100, 1295, 11256, 110964, 1713720, 27147285, 409295260, 7192099486, 146953847404, 3083283003255, 67579239087920, 1632183291677800, 42282787050941616, 1140103579166365929, 32452333261311639540, 982975683671186407090, 31244119064026146137860

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A213644, A370986.

Cf. A346889, A370931.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^3/6*exp(x)))/x))

PARI

a(n) = sum(k=0, n\3, k^(n-3*k)*(n+k)!/(6^k*k!*(n-3*k)!))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} k^(n-3*k) * (n+k)!/(6^k * k! * (n-3*k)!).