A352435 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n,2*k+1) * a(k) * a(n-2*k-1).

1, 1, 2, 7, 32, 182, 1244, 9919, 90384, 926552, 10553728, 132231446, 1807390960, 26762801828, 426771821000, 7291604699407, 132885997278944, 2573145015936096, 52756125043795232, 1141727892772848248, 26009303834699461248, 622134297287753003008, 15589886235793001142016

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

E.g.f.: 1 / (1 - Sum_{n>=0} a(n) * x^(2*n+1) / (2*n+1)!).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 2 k + 1] a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 22}]

Crossrefs

Cf. A138314, A352436, A352437.

Sequence in context: A198891 A000153 A006154 * A000987 A006957 A189780

Adjacent sequences: A352432 A352433 A352434 * A352436 A352437 A352438

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 16 2022

Status

approved