A104670 a(n) = binomial(n+2, 2)*binomial(n+7, n).

1, 24, 216, 1200, 4950, 16632, 48048, 123552, 289575, 629200, 1283568, 2482272, 4585308, 8139600, 13953600, 23193984, 37509021, 59183784, 91333000, 138138000, 205134930, 299562120, 430775280, 610740000, 854611875, 1181415456, 1614834144, 2184124096, 2925166200

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

G.f.: (1 + 14*x + 21*x^2)/(1-x)^10. - Colin Barker, Mar 18 2012

From Amiram Eldar, Aug 30 2022: (Start)

Sum_{n>=0} 1/a(n) = 49*Pi^2/3 - 288281/1800.

Sum_{n>=0} (-1)^n/a(n) = 448*log(2)/3 - 35*Pi^2/6 - 1799/40. (End)

Example

If n=0 then C(2+0,2)*C(7+0,0+0) = C(2,2)*C(7,0) = 1*1 = 1;
if n=6 then C(2+6,2)*C(7+6,0+6) = C(8,2)*C(13,6) = 28*1716 = 48048.

Maple

[seq(stirling2(n+1, n)*binomial(n+6, 7), n=1..25)]; # Zerinvary Lajos, Dec 06 2006

Mathematica

a[n_] := Binomial[n + 2, 2] * Binomial[n + 7, 7]; Array[a, 25, 0] (* Amiram Eldar, Aug 30 2022 *)

Crossrefs

Cf. A062190.

Cf. A000217, A000580.

Sequence in context: A221434 A008655 A133754 * A205968 A232474 A205816

Adjacent sequences: A104667 A104668 A104669 * A104671 A104672 A104673

Keyword

easy,nonn

Author

Zerinvary Lajos, Apr 22 2005

Extensions

Corrected and extended by Don Reble, Nov 21 2006

Status

approved