A076006 Sixth column of triangle A075503.

1, 168, 17024, 1354752, 93499392, 5881430016, 346987429888, 19548208103424, 1064285732077568, 56464495286943744, 2936605030892961792, 150373246607730671616, 7606369972746352328704, 381025640076812853706752

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..5} (A075513(6,m)*exp(8*(m+1)*x))/5!.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..593

Crossrefs

Cf. A076005, A076007.

Programs

Mathematica

With[{m = 6}, Array[8^(# - m) StirlingS2[#, m] &, 14, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075503 *)

Formula

a(n) = A075503(n+6, 6) = (8^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..5} (A075513(6, m)*((m+1)*8)^n)/5!.

G.f.: 1/Product_{k=1..6} (1 - 8*k*x).

E.g.f.: (d^6/dx^6)(((exp(8*x)-1)/8)^6)/6! = (-exp(8*x) + 160*exp(16*x) - 2430*exp(24*x) + 10240*exp(32*x) - 15625*exp(40*x) + 7776*exp(48*x))/5!.