A381444 Expansion of e.g.f. ( (1/x) * Series_Reversion( x * exp(-2*x * cosh(x)) ) )^(1/2).

1, 1, 5, 52, 837, 18276, 504673, 16871632, 662646281, 29912003344, 1526065495101, 86843677613760, 5454045493422925, 374720831464254016, 27958655248431100313, 2251304544037066606336, 194594761915894781438481, 17971382474574151984603392, 1766073848394482007514748533

Offset: 0

Author

Seiichi Manyama, Feb 23 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. A185951, A381143.

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, (2*n+1)^(k-1)*a185951(n, k));

Formula

E.g.f. A(x) satisfies A(x) = exp( x * A(x)^2 * cosh(x * A(x)^2) ).

a(n) = Sum_{k=0..n} (2*n+1)^(k-1) * A185951(n,k).