A370992 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^3/6*(exp(x) - 1)) ).

1, 0, 0, 0, 4, 10, 20, 35, 5656, 55524, 352920, 1801965, 85636540, 1762160686, 22992890284, 232001269955, 6581012518640, 197506018950920, 4224661065644016, 69931313468126169, 1757395269147356340, 60785516594782517650, 1818493252905482003620

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A370988, A370991.

Cf. A353999.

Programs

PARI

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

PARI

a(n) = sum(k=0, n\4, (n+k)!*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (n+k)! * Stirling2(n-3*k,k)/(6^k * (n-3*k)!).