A371836 a(n) = Sum_{k=0..floor(n/2)} n^k * binomial(2*n-2*k-1,n-2*k).

1, 1, 5, 19, 91, 426, 2190, 11467, 63811, 365806, 2200978, 13677962, 88553726, 591576220, 4093814812, 29164567635, 214244414371, 1616044475734, 12523774634922, 99418836782602, 808492937082410, 6720935024074092, 57100849909374340, 495022008799053006

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = [x^n] 1/((1-n*x^2) * (1-x)^n).

a(n) ~ exp(sqrt(n) + 1/2) * n^(n/2) / 2. - Vaclav Kotesovec, Apr 08 2024

Mathematica

Join[{1}, Table[Sum[n^k*Binomial[2*n-2*k-1, n-1], {k, 0, n/2}], {n, 1, 25}]] (* Vaclav Kotesovec, Apr 08 2024 *)

Prog

(PARI) a(n) = sum(k=0, n\2, n^k*binomial(2*n-2*k-1, n-2*k));

Crossrefs

Cf. A293574, A371837.

Cf. A371798, A371826.

Sequence in context: A149806 A149807 A149808 * A149809 A263245 A346199

Adjacent sequences: A371833 A371834 A371835 * A371837 A371838 A371839

Keyword

nonn

Author

Seiichi Manyama, Apr 08 2024

Status

approved