A107398 - OEIS

%I #12 Feb 07 2025 20:04:55

%S 36,960,11880,95040,566280,2718144,11042460,39262080,125147880,

%T 364066560,979945824,2466996480,5859116640,13220570880,28506855960,

%U 59025960576,117846969900,227667211200,426876021000,778861512000,1386019463400,2410468632000,4104188068500

%N a(n) = binomial(n+7, 7) * binomial(n+9, 7).

%H Andrew Howroyd, <a href="/A107398/b107398.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

%F From _Amiram Eldar_, Sep 01 2022: (Start)

%F Sum_{n>=0} 1/a(n) = 8085*Pi^2/2 - 12767311/320.

%F Sum_{n>=0} (-1)^n/a(n) = 245*Pi^2/4 - 580307/960. (End)

%F G.f.: 12*(3 + 35*x + 105*x^2 + 105*x^3 + 35*x^4 + 3*x^5)/(1-x)^15. - _G. C. Greubel_, Feb 07 2025

%e If n=0 then C(n+7,7)*C(n+9,7) = C(7,7)*C(9,7) = 1*36 = 36.

%e If n=4 then C(4+7,7)*C(4+9,7) = C(11,7)*C(13,7) = 330*1716 = 566280.

%t a[n_] := Binomial[n + 7, 7] * Binomial[n + 9, 7]; Array[a, 25, 0] (* _Amiram Eldar_, Sep 01 2022 *)

%o (PARI) a(n)={binomial(n+7, 7) * binomial(n+9, 7)} \\ _Andrew Howroyd_, Nov 08 2019

%o (Magma)

%o A107398:= func< n | Binomial(n+7,7)*Binomial(n+9,7) >;

%o [A107398(n): n in [0..30]]; // _G. C. Greubel_, Feb 07 2025

%o (SageMath)

%o def A107398(n): return binomial(n+7,7)*binomial(n+9,7)

%o print([A107398(n) for n in range(31)]) # _G. C. Greubel_, Feb 07 2025

%Y Cf. A062196.

%K easy,nonn,changed

%O 0,1

%A _Zerinvary Lajos_, May 25 2005

%E a(3) corrected and terms a(8) and beyond from _Andrew Howroyd_, Nov 08 2019