A091364 a(n) = n! * n^4.

0, 1, 32, 486, 6144, 75000, 933120, 12101040, 165150720, 2380855680, 36288000000, 584421868800, 9932577177600, 177849941068800, 3349041234739200, 66201014880000000, 1371195958099968000, 29707369682006016000

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,4,1) - ((gamma^4/24+Pi^2*gamma^2/24+zeta(3)*gamma/3+Pi^4/160) + (gamma^3/6+ Pi^2*gamma/12+ zeta(3)/3)*log(x) + (gamma^2/4+ Pi^2/24)*log(x)^2 + (gamma/6)*log(x)^3 + log(x)^4/24), 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!), A091363 (n^3*n!). - Johannes W. Meijer, Oct 16 2009

Programs

Maple

a:=n->sum(sum(sum((n+1)!-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^4, {n, 0, 20}]

Formula

E.g.f.: (x + 11x^2 + 11x^3 + x^4)/(1 - x)^5

Extensions

More terms from Zerinvary Lajos, May 16 2007