A075512 Seventh column of triangle A075497.

1, 56, 1848, 47040, 1023792, 20076672, 365787136, 6314147840, 104637781248, 1680323893248, 26325099300864, 404403166003200, 6115019304300544, 91287994741981184, 1348582723009708032

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(2*(m+1)*x)/6!.

Crossrefs

Cf. A075511.

Formula

a(n) = A075497(n+7, 7) = (2^n)*S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..6} A075513(7, m)*((m+1)*2)^n/6!.

G.f.: 1/Product_{k=1..7} (1 - 2*k*x).

E.g.f.: (d^7/dx^7)(((exp(2*x)-1)/2)^7)/7! = (exp(2*x) - 384*exp(4*x) + 10935*exp(6*x) - 81920*exp(8*x) + 234375*exp(10*x) - 279936*exp(12*x) + 117649*exp(14*x))/6!.