A075923 Fourth column of triangle A075502.

1, 70, 3185, 120050, 4084101, 130590390, 4012419145, 120031392250, 3525181576301, 102196720335710, 2935410756419505, 83751552660170850, 2377917929557166101, 67273652916778177030, 1898215473677945050265

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..3} A075513(4,m)*exp(7*(m+1)*x)/3!.

Crossrefs

Cf. A075922, A075924.

Formula

a(n) = A075502(n+4, 4) = (7^n)*S2(n+4, 4) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = (-7^n + 24*14^n - 81*21^n + 64*28^n)/3!.

G.f.: 1/Product_{k=1..4} (1 - 7*k*x).

E.g.f.: (d^4/dx^4)(((exp(7*x)-1)/7)^4)/4! = (-exp(7*x) + 24*exp(14*x) - 81*exp(21*x) + 64*exp(28*x))/3!.