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
Examples
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.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Magma
A104676:= func< n | Binomial(n+2,2)*Binomial(n+7,2) >; [A104676(n): n in [0..50]]; // G. C. Greubel, Mar 01 2025
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Maple
A104676:=n->binomial(n+2,2)*binomial(n+7,2): seq(A104676(n), n=0..50); # Wesley Ivan Hurt, Mar 30 2017
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Mathematica
Table[Binomial[n + 2, 2] Binomial[n + 7, 2], {n, 0, 37}] (* Michael De Vlieger, Nov 29 2015 *) -
PARI
a(n) = binomial(n+2,2)*binomial(n+7,2); \\ Michel Marcus, Nov 29 2015
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SageMath
def A104676(n): return binomial(n+2,2)*binomial(n+7,2) print([A104676(n) for n in range(51)]) # G. C. Greubel, Mar 01 2025
Formula
From R. J. Mathar, Nov 29 2015: (Start)
G.f.: 3*(7 - 7*x + 2*x^2)/(1-x)^5. (End)
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)
E.g.f.: (1/4)*(84 + 252*x + 138*x^2 + 22*x^3 + x^4)*exp(x). - G. C. Greubel, Mar 01 2025