A076004 Fourth column of triangle A075503.

1, 80, 4160, 179200, 6967296, 254607360, 8940421120, 305659904000, 10259284361216, 339910422691840, 11158051230842880, 363834840082022400, 11805930580539867136, 381715961976738283520, 12309283295632755261440

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(8*(m+1)*x)/3!.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..663

Crossrefs

Cf. A076003, A076005.

Programs

Mathematica

With[{m = 4}, Array[8^(# - m) StirlingS2[#, m] &, 15, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075503 *)

Formula

a(n) = A075503(n+4, 4) = (8^n)*S2(n+4, 4) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..3} ((A075513(4, m)*(m+1)*8)^n)/3!.

G.f.: 1/Product_{k=1..4} (1 - 8*k*x).

E.g.f.: (d^4/dx^4)(((exp(8*x)-1)/8)^4)/4! = (-exp(8*x) + 24*exp(16*x) - 81*exp(24*x) + 64*exp(32*x))/3!.