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
Examples
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.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
Programs
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Magma
A104670:= func< n | Binomial(n+2,n)*Binomial(n+7,n) >; [A104670(n): n in [0..30]]; // G. C. Greubel, Mar 01 2025
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Maple
[seq(stirling2(n+1,n)*binomial(n+6,7),n=1..25)]; # Zerinvary Lajos, Dec 06 2006
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Mathematica
a[n_] := Binomial[n + 2, 2] * Binomial[n + 7, 7]; Array[a, 25, 0] (* Amiram Eldar, Aug 30 2022 *)
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SageMath
def A104670(n): return binomial(n+2,n)*binomial(n+7,n) print([A104670(n) for n in range(31)]) # G. C. Greubel, Mar 01 2025
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)
Extensions
Corrected and extended by Don Reble, Nov 21 2006