A380914 E.g.f. A(x) satisfies A(x) = exp(x / (1 - x*A(x))) / (1 - x*A(x)).

1, 2, 11, 115, 1797, 37621, 990313, 31452905, 1171010809, 50029903081, 2413119476781, 129719605920565, 7690829719605541, 498579900892422077, 35086898369381747281, 2663953520081549084401, 217057092837921132411249, 18892120969438125131207377, 1749385548844357561820688853

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

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

Prog

(PARI) a(n, q=1, r=1, s=0, t=1, u=1) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial((r*u+1)*n+((s-r)*u+t-1)*k+q*u-1, n-k)/k!);

Crossrefs

Cf. A380769, A380915.

Cf. A380663.

Sequence in context: A181168 A269082 A378016 * A304639 A374140 A130222

Adjacent sequences: A380911 A380912 A380913 * A380915 A380916 A380917

Keyword

nonn

Author

Seiichi Manyama, Feb 08 2025

Status

approved