A381179 E.g.f. A(x) satisfies A(x) = 1 + sinh(x*A(x)) / A(x).

1, 1, 0, 1, 8, 21, 64, 1093, 8448, 47785, 654848, 9402537, 94222336, 1264390141, 23392960512, 363389219053, 5722054885376, 117602664867921, 2434091053613056, 47867013812467921, 1080303165427679232, 26716998341391367141, 645003218568158904320, 16403742152044108508181

Offset: 0

Author

Seiichi Manyama, Feb 16 2025

Keywords

• nonn

Crossrefs

Cf. A162653, A201628, A381177.

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

Formula

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