A381382 E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)^2) / A(x)^2 ).

1, 1, 2, 7, 48, 541, 7600, 120891, 2178176, 45053401, 1065957888, 28344376303, 831973593088, 26647344263541, 925300511922176, 34668496386129763, 1394928344160731136, 59986286728056665905, 2744940504174063714304, 133158543838350039763671

Offset: 0

Author

Seiichi Manyama, Feb 22 2025

Keywords

• nonn

Crossrefs

Cf. A364980, A381376, A381378, A381384.

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(2*n-k+1, k)/(2*n-k+1)*a136630(n, k));

Formula

a(n) = Sum_{k=0..n} k! * binomial(2*n-k+1,k)/(2*n-k+1) * A136630(n,k).