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

Author

Peter Bala, Oct 12 2011

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A007318, A197208.

Programs

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 *)

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

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