A197209 Row sums of A197208.

3, 24, 180, 1320, 9660, 70896, 522648, 3871440, 28809990, 215318400, 1615579680, 12165491520, 91905439080, 696359055840, 5290416835440, 40291036122528, 307537305284574, 2352216447006480, 18024996856976760

Offset

2,1

Links

Seiichi Manyama, Table of n, a(n) for n = 2..1000

Formula

For n >= 2, a(n) = Sum_{k = 1..n-1} C(n-1,k-1)*C(n,k+1)*C(n+1,k), where C(n,k) = binomial(n,k).

a(n) = (1/(n+2)) * ((7*n^2-7*n-2)*a(n-1)/(n-2) + 8*n*a(n-2)) for n > 3. - Seiichi Manyama, Jan 09 2021

Mathematica

Table[Sum[Binomial[n-1, k-1]Binomial[n, k+1]Binomial[n+1, k], {k, n-1}], {n, 2, 20}] (* Harvey P. Dale, May 08 2016 *)

Prog

(PARI) a(n) = sum(k=1, n-1, binomial(n-1, k-1)*binomial(n, k+1)*binomial(n+1, k)); \\ Michel Marcus, Jan 09 2021

Crossrefs

Cf. A007318, A197208.

Sequence in context: A356361 A292293 A073985 * A317527 A181967 A144087

Adjacent sequences: A197206 A197207 A197208 * A197210 A197211 A197212

Keyword

nonn,easy

Author

Peter Bala, Oct 12 2011

Status

approved