A107396 a(n) = binomial(n+5, 5) * binomial(n+7, 5).
21, 336, 2646, 14112, 58212, 199584, 594594, 1585584, 3864861, 8744736, 18582564, 37425024, 71954064, 132838272, 236618172, 408282336, 684723501, 1119300336, 1787771370, 2795913120, 4289184900, 6464858400, 9587091150, 14005489680, 20177780805, 28697288256
Offset: 0
Examples
If n=0 then C(0+5,5)*C(0+7,5) = C(5,5)*C(7,5) = 1*21 = 21. If n=9 then C(6+5,5)*C(6+7,5) = C(11,5)*C(13,5) = 462*1287 = 594594.
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
Programs
-
Magma
A107396:= func< n | Binomial(n+5,5)*Binomial(n+7,5) >; [A107396(n): n in [0..30]]; // G. C. Greubel, Feb 09 2025
-
Mathematica
a[n_] := Binomial[n + 5, 5] * Binomial[n + 7, 5]; Array[a, 25, 0] (* Amiram Eldar, Sep 01 2022 *)
-
PARI
a(n)={binomial(n+5, 5) * binomial(n+7, 5)} \\ Andrew Howroyd, Nov 08 2019 -
SageMath
def A107396(n): return binomial(n+5,5)*binomial(n+7,5) print([A107396(n) for n in range(31)]) # G. C. Greubel, Feb 09 2025
Formula
From Amiram Eldar, Sep 01 2022: (Start)
Sum_{n>=0} 1/a(n) = 350*Pi^2/3 - 82901/72.
Sum_{n>=0} (-1)^n/a(n) = 1975/24 - 25*Pi^2/3. (End)
G.f.: 21*(1 + 5*x + 5*x^2 + x^3)/(1-x)^11. - G. C. Greubel, Feb 09 2025
Extensions
a(7) corrected and terms a(15) and beyond from Andrew Howroyd, Nov 08 2019