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%I #22 Aug 30 2022 09:44:11
%S 21,84,216,450,825,1386,2184,3276,4725,6600,8976,11934,15561,19950,
%T 25200,31416,38709,47196,57000,68250,81081,95634,112056,130500,151125,
%U 174096,199584,227766,258825,292950,330336,371184,415701,464100,516600,573426,634809,700986
%N a(n) = binomial(n+2,2) * binomial(n+7,2).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = A000217(n+1) * A000217(n+6). - _R. J. Mathar_, Nov 29 2015
%F G.f.: 3*( -7+7*x-2*x^2 ) / (x-1)^5. - _R. J. Mathar_, Nov 29 2015
%F a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - _Wesley Ivan Hurt_, Jan 25 2022
%F From _Amiram Eldar_, Aug 30 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 7/100.
%F Sum_{n>=0} (-1)^n/a(n) = 7/180. (End)
%e If n=0 then C(0+2,0+0)*C(0+7,2) = C(2,0)*C(7,2) = 1*21 = 21.
%e If n=8 then C(8+2,8+0)*C(8+7,2) = C(10,8)*C(15,2) = 45*105 = 4725.
%p A104676:=n->binomial(n+2,2)*binomial(n+7,2): seq(A104676(n), n=0..50); # _Wesley Ivan Hurt_, Mar 30 2017
%t Table[Binomial[n + 2, 2] Binomial[n + 7, 2], {n, 0, 37}] (* _Michael De Vlieger_, Nov 29 2015 *)
%o (PARI) a(n) = binomial(n+2,2)*binomial(n+7,2); \\ _Michel Marcus_, Nov 29 2015
%Y Cf. A000217, A062190.
%Y Subsequence of A085780.
%K easy,nonn
%O 0,1
%A _Zerinvary Lajos_, Apr 22 2005
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