A381478 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x) * cosh(x * A(x)) )^2.

1, 2, 14, 186, 3696, 98290, 3283920, 132311354, 6246905728, 338374946466, 20688891816960, 1409607482926522, 105914955915952128, 8701156803022552466, 775923181679913938944, 74646655589398509637050, 7706371729268071660093440, 849834260414107910987980354

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, A377546, A381387, A381449, A381477.

Programs

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381477.

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

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