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%I #21 Sep 08 2022 08:45:12
%S 0,1,16,162,1536,15000,155520,1728720,20643840,264539520,3628800000,
%T 53129260800,827714764800,13680764697600,239217231052800,
%U 4413400992000000,85699747381248000,1747492334235648000,37338643451805696000,834363743704178688000
%N a(n) = n!*n^3.
%C Denominators in the power series expansion of the higher order exponential integral E(x,3,1) + (gamma^3/6+Pi^2*gamma/36+zeta(3)/3+Pi^2*gamma/18) + (gamma^2/2+Pi^2/12)*log(x) + gamma*log(x)^2/2 + log(x)^3/6, n>0. See A163931 for information on the E(x,m,n). - _Johannes W. Meijer_, Oct 16 2009
%F E.g.f.: (x+4x^2+x^3)/(1-x)^4.
%p a:=n->sum(sum(sum((n!), j=1..n),k=1..n),m=1..n): seq(a(n), n=0..17); # _Zerinvary Lajos_, May 16 2007
%t Table[n!n^3, {n, 0, 20}]
%o (Magma) [Factorial(n)*n^3: n in [0..40]]; // _Vincenzo Librandi_, Jun 25 2015
%Y Cf. A163931 (E(x,m,n)), A001563 (n*n!), A002775 (n^2*n!), A091364 (n^4*n!). - _Johannes W. Meijer_, Oct 16 2009
%K easy,nonn
%O 0,3
%A Mario Catalani (mario.catalani(AT)unito.it), Jan 07 2004
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