A075916 Third column of triangle A075501.

1, 36, 900, 19440, 390096, 7511616, 141134400, 2611802880, 47870735616, 871982724096, 15819463296000, 286235993272320, 5170077903015936, 93275375604350976, 1681524519443251200, 30298254922942709760

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..2} A075513(3,m)*exp(6*(m+1)*x)/2!.

Crossrefs

Cf. A016175, A075917.

Formula

a(n) = A075501(n+3, 3) = (6^n)*S2(n+3, 3) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = (6^n - 8*12^n + 9*18^n)/2.

G.f.: 1/Product_{k=1..3} (1 - 6*k*x).

E.g.f.: (d^3/dx^3)(((exp(6*x)-1)/6)^3)/3! = (exp(6*x) - 8*exp(12*x) + 9*exp(18*x))/2!.