A075922 Third column of triangle A075502.

1, 42, 1225, 30870, 722701, 16235562, 355888225, 7683656190, 164302593301, 3491636199282, 73902587019625, 1560051480424710, 32874455072382301, 691950889177526202, 14553192008156093425, 305928163614832076430

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(7*(m+1)*x)/2!.

Crossrefs

Cf. A075921, A075923.

Formula

a(n) = A075502(n+3, 3) = (7^n)*S2(n+3, 3) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = (7^n - 8*14^n + 9*21^n)/2.

G.f.: 1/Product_{k=1..3} (1 - 7*k*x).

E.g.f.: (d^3/dx^3)(((exp(7*x)-1)/7)^3)/3! = (exp(7*x) - 8*exp(14*x) + 9*exp(21*x))/2!.