A370991 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^2/2*(exp(x) - 1)) ).

1, 0, 0, 3, 6, 10, 735, 5691, 29428, 1122696, 18159165, 190810675, 5768268726, 143497346928, 2479363382587, 73013461310895, 2336253676913640, 58015822633914736, 1850758447642034553, 69357415099500398979, 2252468410247071488970

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A370988, A370992.

Cf. A353998.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2/2*(exp(x)-1)))/x))

PARI

a(n) = sum(k=0, n\3, (n+k)!*stirling(n-2*k, k, 2)/(2^k*(n-2*k)!))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (n+k)! * Stirling2(n-2*k,k)/(2^k * (n-2*k)!).