A298700 a(n) = (n/2)*Sum_{k=1..n} C(n + k, n)*C(k, n - k)/k.

1, 6, 25, 120, 581, 2877, 14421, 72996, 372229, 1909336, 9840909, 50923041, 264391973, 1376654747, 7185811685, 37589283916, 197005160825, 1034244838815, 5437798710585, 28629290831670, 150913830095445, 796396974477495, 4206974157985845, 22243990866224505

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Maple

a := n -> (n/2)*add(binomial(n + k, n)*binomial(k, n - k)/k, k=1..n):
seq(a(n), n=1..24);
# Alternatively:
a := n -> `if`(n mod 2=0, 1, n/2)*binomial(2*n - floor(n/2), ceil(n/2))*hypergeom(
[-floor(n/2), ceil(n/2), floor(3*(n+1)/2)], [n mod 2+1/2, ceil(n/2)+1], -1/4):
seq(simplify(a(n)), n=1..24);

Mathematica

Table[n/2 Sum[Binomial[n+k, n] Binomial[k, n-k]/k, {k, n}], {n, 30}] (* Harvey P. Dale, Dec 29 2021 *)

Prog

(PARI) a(n) = (n/2)*sum(k=1, n, binomial(n+k, n)*binomial(k, n-k)/k); \\ Michel Marcus, Jan 27 2018

Crossrefs

Sequence in context: A120758 A227914 A179603 * A215763 A153481 A099359

Adjacent sequences: A298697 A298698 A298699 * A298701 A298702 A298703

Keyword

nonn

Author

Peter Luschny, Jan 26 2018

Status

approved