A075910 Seventh column of triangle A075499.

1, 112, 7392, 376320, 16380672, 642453504, 23410376704, 808210923520, 26787271999488, 860325833342976, 26956901684084736, 828217683974553600, 25047119070415028224, 747831252926309859328, 22095179333791056396288

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

Crossrefs

Cf. A075509.

Programs

Mathematica

CoefficientList[Series[1/Product[1-4k x,{k,7}],{x,0,20}],x] (* Harvey P. Dale, Aug 11 2021 *)

Formula

a(n) = A075499(n+7, 7) = (4^n)*S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..6} A075513(7, m)*((m+1)*4)^n/6!.

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

E.g.f.: (d^7/dx^7)(((exp(4*x)-1)/4)^7)/7! = (exp(4*x) - 384*exp(8*x) + 10935*exp(12*x) - 81920*exp(16*x) + 234375*exp(20*x) - 279936*exp(24*x) + 117649*exp(28*x))/6!.