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

0,1

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).

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

Example

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.

Mathematica

a[n_] := Binomial[n + 5, 5] * Binomial[n + 7, 5]; Array[a, 25, 0] (* Amiram Eldar, Sep 01 2022 *)

Prog

(PARI) a(n)={binomial(n+5, 5) * binomial(n+7, 5)} \\ Andrew Howroyd, Nov 08 2019
(Magma)
A107396:= func< n | Binomial(n+5, 5)*Binomial(n+7, 5) >;
[A107396(n): n in [0..30]]; // G. C. Greubel, Feb 09 2025
(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

Crossrefs

Cf. A033987, A062196.

Sequence in context: A297336 A095905 A051525 * A036224 A113895 A062260

Adjacent sequences: A107393 A107394 A107395 * A107397 A107398 A107399

Keyword

easy,nonn,changed

Author

Zerinvary Lajos, May 25 2005

Extensions

a(7) corrected and terms a(15) and beyond from Andrew Howroyd, Nov 08 2019

Status

approved