A075515 Fifth column of triangle A075498.

1, 45, 1260, 28350, 563031, 10333575, 179866170, 3016747800, 49263275061, 788796913905, 12445575859080, 194186867360850, 3004103990159091, 46168557763591035, 705914973500103990, 10750288516418083500

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(3*(m+1)*x)/4!.

Crossrefs

Cf. A028085, A075516.

Formula

a(n) = A075498(n+5, 5) = (3^n)*S2(n+5, 5) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..4} A075513(5, m)*exp((m+1)*3)^n/4!.

G.f.: 1/Product_{k=1..5} (1 - 3*k*x).

E.g.f.: (d^5/dx^5)(((exp(3*x)-1)/3)^5)/5! = (exp(3*x) - 64*exp(6*x) + 486*exp(9*x) - 1024*exp(12*x) + 625*exp(15*x))/4!.