A076003 Third column of triangle A075503.

1, 48, 1600, 46080, 1232896, 31653888, 792985600, 19566428160, 478167433216, 11613323132928, 280917704704000, 6777200695050240, 163215697915150336, 3926183399462535168, 94372512377130188800

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..2} A075513(3,m)*exp(8*(m+1)*x)/2!.

Crossrefs

Cf. A060195, A076004.

Formula

a(n) = A075503(n+3, 3) = (8^n)*S2(n+3, 3) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = (8^n - 8*16^n + 9*24^n)/2.

G.f.: 1/Product_{k=1..3} (1 - 8*k*x).

E.g.f.: (d^3/dx^3)(((exp(8*x)-1)/8)^3)/3! = (exp(8*x) - 8*exp(16*x) + 9*exp(24*x))/2!.