A381477 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x)^2 * cosh(x * A(x)^2) ).

1, 1, 6, 75, 1440, 37445, 1231440, 49037527, 2294425728, 123393443049, 7500623201280, 508577491719011, 38057966976387072, 3115680296111519149, 277005128553759191040, 26579020362900758232495, 2737628961211699538657280, 301278578823933606439917137, 35281158151116225085977526272

Offset: 0

Author

Seiichi Manyama, Feb 24 2025

Keywords

• nonn

Comments

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

Crossrefs

Cf. A185951, A364985, A381386.

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, k!*binomial(2*n+k+1, k)/(2*n+k+1)*a185951(n, k));

Formula

a(n) = Sum_{k=0..n} k! * binomial(2*n+k+1,k)/(2*n+k+1) * A185951(n,k).

E.g.f.: ( (1/x) * Series_Reversion( x*(1 - x*cosh(x))^2 ) )^(1/2).