A091363 a(n) = n!*n^3.

0, 1, 16, 162, 1536, 15000, 155520, 1728720, 20643840, 264539520, 3628800000, 53129260800, 827714764800, 13680764697600, 239217231052800, 4413400992000000, 85699747381248000, 1747492334235648000, 37338643451805696000, 834363743704178688000

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Jan 07 2004

Keywords

• easy
• nonn

Comments

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

Crossrefs

Cf. A163931 (E(x,m,n)), A001563 (n*n!), A002775 (n^2*n!), A091364 (n^4*n!). - Johannes W. Meijer, Oct 16 2009

Programs

Magma

[Factorial(n)*n^3: n in [0..40]]; // Vincenzo Librandi, Jun 25 2015

Maple

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

Mathematica

Table[n!n^3, {n, 0, 20}]

Formula

E.g.f.: (x+4x^2+x^3)/(1-x)^4.