A104670 - OEIS

%I #25 Aug 30 2022 09:43:42

%S 1,24,216,1200,4950,16632,48048,123552,289575,629200,1283568,2482272,

%T 4585308,8139600,13953600,23193984,37509021,59183784,91333000,

%U 138138000,205134930,299562120,430775280,610740000,854611875,1181415456,1614834144,2184124096,2925166200

%N a(n) = binomial(n+2, 2)*binomial(n+7, n).

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F G.f.: (1 + 14*x + 21*x^2)/(1-x)^10. - _Colin Barker_, Mar 18 2012

%F From _Amiram Eldar_, Aug 30 2022: (Start)

%F Sum_{n>=0} 1/a(n) = 49*Pi^2/3 - 288281/1800.

%F Sum_{n>=0} (-1)^n/a(n) = 448*log(2)/3 - 35*Pi^2/6 - 1799/40. (End)

%e If n=0 then C(2+0,2)*C(7+0,0+0) = C(2,2)*C(7,0) = 1*1 = 1;

%e if n=6 then C(2+6,2)*C(7+6,0+6) = C(8,2)*C(13,6) = 28*1716 = 48048.

%p [seq(stirling2(n+1,n)*binomial(n+6,7),n=1..25)]; # _Zerinvary Lajos_, Dec 06 2006

%t a[n_] := Binomial[n + 2, 2] * Binomial[n + 7, 7]; Array[a, 25, 0] (* _Amiram Eldar_, Aug 30 2022 *)

%Y Cf. A062190.

%Y Cf. A000217, A000580.

%K easy,nonn

%O 0,2

%A _Zerinvary Lajos_, Apr 22 2005

%E Corrected and extended by _Don Reble_, Nov 21 2006