A104676 a(n) = binomial(n+2,2) * binomial(n+7,2).

21, 84, 216, 450, 825, 1386, 2184, 3276, 4725, 6600, 8976, 11934, 15561, 19950, 25200, 31416, 38709, 47196, 57000, 68250, 81081, 95634, 112056, 130500, 151125, 174096, 199584, 227766, 258825, 292950, 330336, 371184, 415701, 464100, 516600, 573426, 634809, 700986

Offset

0,1

Links

Table of n, a(n) for n=0..37.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = A000217(n+1) * A000217(n+6). - R. J. Mathar, Nov 29 2015

G.f.: 3*( -7+7*x-2*x^2 ) / (x-1)^5. - R. J. Mathar, Nov 29 2015

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Wesley Ivan Hurt, Jan 25 2022

From Amiram Eldar, Aug 30 2022: (Start)

Sum_{n>=0} 1/a(n) = 7/100.

Sum_{n>=0} (-1)^n/a(n) = 7/180. (End)

Example

If n=0 then C(0+2,0+0)*C(0+7,2) = C(2,0)*C(7,2) = 1*21 = 21.
If n=8 then C(8+2,8+0)*C(8+7,2) = C(10,8)*C(15,2) = 45*105 = 4725.

Maple

A104676:=n->binomial(n+2, 2)*binomial(n+7, 2): seq(A104676(n), n=0..50); # Wesley Ivan Hurt, Mar 30 2017

Mathematica

Table[Binomial[n + 2, 2] Binomial[n + 7, 2], {n, 0, 37}] (* Michael De Vlieger, Nov 29 2015 *)

Prog

(PARI) a(n) = binomial(n+2, 2)*binomial(n+7, 2); \\ Michel Marcus, Nov 29 2015

Crossrefs

Cf. A000217, A062190.

Subsequence of A085780.

Sequence in context: A190023 A071397 A064762 * A143244 A041856 A044208

Adjacent sequences: A104673 A104674 A104675 * A104677 A104678 A104679

Keyword

easy,nonn

Author

Zerinvary Lajos, Apr 22 2005

Status

approved