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%I #17 Aug 30 2022 09:44:30
%S 792,13728,123552,772200,3775200,15402816,54609984,172931616,
%T 498841200,1330243200,3316739712,7801876368,17439488352,37263864000,
%U 76488984000,151448188320,290275694280,540192201120,978609060000,1729734435000,2988981103680,5058275713920
%N a(n) = binomial(n+7,7)*binomial(n+12,7).
%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 G.f.: -264*(3+7*x+3*x^2)/(x-1)^15. - _R. J. Mathar_, Nov 29 2015
%F From _Amiram Eldar_, Aug 30 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 1263966463/1306800 - 98*Pi^2.
%F Sum_{n>=0} (-1)^n/a(n) = 3935051/13068 - 14336*log(2)/33. (End)
%e If n=0 then C(0+7,0+0)*C(0+12,7) = C(7,0)*C(12,7) = 1*792 = 792.
%e If n=6 then C(6+7,6+0)*C(6+12,7) = C(13,6)*C(18,7) = 1716*32824 = 54609984.
%t a[n_] := Binomial[n + 7, 7] * Binomial[n + 12, 7]; Array[a, 25, 0] (* _Amiram Eldar_, Aug 30 2022 *)
%Y Cf. A062190.
%K easy,nonn
%O 0,1
%A _Zerinvary Lajos_, Apr 22 2005