A075908 Fifth column of triangle A075499.

1, 60, 2240, 67200, 1779456, 43545600, 1010606080, 22600089600, 492077121536, 10505429975040, 221005133905920, 4597756408627200, 94837435443183616, 1943344895628410880, 39618196941842677760

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..4} A075513(5,m)*exp(4*(m+1)*x)/4!.

Crossrefs

Cf. A075907, A075909.

Formula

a(n) = A075499(n+5, 5) = (4^n)*S2(n+5, 5) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..4} A075513(5, m)*((m+1)*4)^n/4!.

G.f.: 1/Product_{k=1..5} (1 - 4*k*x).

E.g.f.: (d^5/dx^5)(((exp(4*x)-1)/4)^5)/5! = (exp(4*x) - 64*exp(8*x) + 486*exp(12*x) - 1024*exp(16*x) + 625*exp(20*x))/4!.