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a(n) = (n+1)^3*(3+n)!/6.
3

%I #21 Sep 08 2022 08:45:40

%S 1,32,540,7680,105000,1451520,20744640,309657600,4849891200,

%T 79833600000,1381360780800,25107347865600,478826764416000,

%U 9568689242112000,200074178304000000,4370687116443648000,99607063051431936000

%N a(n) = (n+1)^3*(3+n)!/6.

%C Row 3 of square array A152818.

%H Vincenzo Librandi, <a href="/A154306/b154306.txt">Table of n, a(n) for n = 0..200</a>

%F E.g.f.: (1 + 25*x + 67*x^2 + 27*x^3)/(1-x)^7. - _R. J. Mathar_, Dec 21 2011

%t Table[(n+1)^3*(3+n)!/6,{n,0,20}] (* _Vincenzo Librandi_, Mar 27 2012 *)

%o (Magma) [(n+1)^3*Factorial(3+n)/6: n in [0..20]]; // _Vincenzo Librandi_, Mar 27 2012

%o (PARI) a(n) = (n+1)^3*(n+3)!/6 \\ _Charles R Greathouse IV_, Sep 10 2016

%Y Cf. A000142, A001563, A055533, A152818, A154307, A154308.

%K nonn,easy

%O 0,2

%A _Omar E. Pol_, Jan 06 2009

%E More terms from _Sean A. Irvine_, Dec 01 2009