A381429 E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x) * A(x)^3 ).

1, 1, 8, 133, 3392, 117601, 5167808, 275334613, 17250670592, 1242994578721, 101273185092608, 9206681997173893, 923928346115182592, 101453787213382443841, 12100018549609932996608, 1557645163271323384461973, 215265839194368088629051392, 31788685348087376561935104961

Offset: 0

Author

Seiichi Manyama, Feb 23 2025

Keywords

• nonn

Crossrefs

Cf. A006154, A295254, A381428.

Cf. A136630.

Programs

PARI

a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, k!*binomial(4*k+1, k)/(4*k+1)*a136630(n, k));

Formula

a(n) = Sum_{k=0..n} k! * binomial(4*k+1,k)/(4*k+1) * A136630(n,k).