A381177 E.g.f. A(x) satisfies A(x) = 1/( 1 - A(x) * sinh(x * A(x)) ).

1, 1, 6, 73, 1352, 33861, 1072000, 41083477, 1849680768, 95708731945, 5597075177984, 365091888890433, 26281788308598784, 2069729710424907181, 177006820644852031488, 16337090667286093559821, 1618592591411194127089664, 171337824188415839421148881, 19299478529228162963028508672

Offset: 0

Author

Seiichi Manyama, Feb 16 2025

Keywords

• nonn

Crossrefs

Cf. A162653, A201628, A381179.

Cf. A136630, A196776.

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

Formula

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