A382043 E.g.f. A(x) satisfies A(x) = 1 + x*A(x)^3*exp(2*x*A(x)).

1, 1, 10, 168, 4280, 146840, 6354432, 332467072, 20419261312, 1440559380096, 114820434103040, 10205253450850304, 1000815286620229632, 107355373421379825664, 12504295470535952613376, 1571670041412254073323520, 212035122185327799251468288, 30561822671438790519426154496

Offset: 0

Author

Seiichi Manyama, Mar 13 2025

Keywords

• nonn

Crossrefs

Cf. A366232, A379690, A382044.

Cf. A364984, A382030.

Programs

PARI

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

Formula

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