A075919 Sixth column of triangle A075501.

1, 126, 9576, 571536, 29583792, 1395690912, 61756307712, 2609370796032, 106548747072768, 4239618914539008, 165370550603102208, 6351034526066700288, 240942052882092847104, 9052126728954680254464

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(6*(m+1)*x)/5!.

Crossrefs

Cf. A075918, A075920.

Formula

a(n) = A075501(n+6, 6) = (6^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).

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

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

E.g.f.: (d^6/dx^6)(((exp(6*x)-1)/6)^6)/6! = (-exp(6*x) + 160*exp(12*x) - 2430*exp(18*x) + 10240*exp(24*x) - 15625*exp(30*x) + 7776*exp(36*x))/5!.