A381143 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * cosh(x)) ).

1, 1, 3, 19, 185, 2381, 38227, 739271, 16752465, 435437209, 12772234211, 417396070235, 15040805940745, 592531894182437, 25336144876513395, 1168670193628654351, 57845446906144852769, 3058248577410499021361, 172007282950136451003331, 10255035157348348977955619

Offset: 0

Author

Seiichi Manyama, Feb 15 2025

Keywords

• nonn

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Links

• Index entries for reversions of series

Crossrefs

Cf. A003727, A162649, A381140.

Cf. A185951.

Programs

PARI

a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, (n+1)^(k-1)*a185951(n, k));

Formula

E.g.f. A(x) satisfies A(x) = exp( x * A(x) * cosh(x * A(x)) ).

a(n) = Sum_{k=0..n} (n+1)^(k-1) * A185951(n,k).