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%I #32 Sep 20 2022 02:02:08
%S 1,64,1000,8000,42875,175616,592704,1728000,4492125,10648000,23393656,
%T 48228544,94196375,175616000,314432000,543338496,909853209,1481544000,
%U 2352637000,3652264000,5554637011,8291469824,12167000000,17576000000,25025203125,35158608576,48787170264
%N a(n) = binomial(n+3,n)^3.
%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.: 3F2(4,4,4;1,1;z).
%F G.f.: (1 + 54x + 405x^2 + 760x^3 + 405x^4 + 54x^5 + x^6)/(x-1)^10.
%F a(n) = (6 + 11n + 6n^2 + n^3)^3/216.
%F a(n) = A000292(n+1)^3.
%F Sum_{n>=0} 1/a(n) = 783/4 - 162*zeta(3). - _Jaume Oliver Lafont_, Jul 17 2017
%F Sum_{n>=0} (-1)^n/a(n) = 1296*log(2) + 405*zeta(3)/2 - 4563/4. - _Amiram Eldar_, Sep 20 2022
%p A270272:=n->binomial(n+3,n)^3: seq(A270272(n), n=0..50); # _Wesley Ivan Hurt_, Jul 17 2017
%t Table[Binomial[n+3,n]^3,{n,0,30}]
%o (PARI) a(n) = binomial(n+3,n)^3; \\ _Michel Marcus_, Jul 17 2017
%Y Cf. A000578, A000292, A001249.
%K nonn,easy
%O 0,2
%A _Benedict W. J. Irwin_, Mar 14 2016