A076002 Seventh column of triangle A075502.

1, 196, 22638, 2016840, 153632787, 10544644572, 672413918176, 40624783239040, 2356312445219733, 132435800821952628, 7261903300743441714, 390447849166013566200, 20663998640254649395639

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..6} A075513(7,m)*exp(7*(m+1)*x)/6!.

Crossrefs

Cf. A075525.

Formula

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

a(n) = Sum_{m=0..6} A075513(7, m)*((m+1)*7)^n/6!.

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

E.g.f.: (d^7/dx^7)(((exp(7*x)-1)/7)^7)/7! = (exp(7*x) - 384*exp(14*x) + 10935*exp(21*x) - 81920*exp(28*x) + 234375*exp(35*x) - 279936*exp(42*x) + 117649*exp(49*x))/6!.