A076010 -id:A076010 - cp's OEIS frontend

A076009 Third column of triangle A075504.

1, 54, 2025, 65610, 1974861, 57041334, 1607609025, 44625100770, 1226874595221, 33521945231214, 912229968911625, 24758714599712730, 670798674525559581, 18153207600055622694, 490886209059873519825

Offset: 0

Wolfdieter Lang, Oct 02 2002

The e.g.f. given below is Sum_{m=0..2} (A075513(3,m)*exp(9*(m+1)*x))/2!.

Michael De Vlieger, Table of n, a(n) for n = 0..698

Cf. A076008, A076010.

With[{m = 3}, Array[9^(# - m) StirlingS2[#, m] &, 15, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075504 *)

a(n) = A075504(n+3, 3) = (9^n)*S2(n+3, 3) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = (9^n - 8*18^n + 9*27^n)/2.
G.f.: 1/Product_{k=1..3} (1 - 9*k*x).
E.g.f.: (d^3/dx^3)(((exp(9*x)-1)/9)^3)/3! = (exp(9*x) - 8*exp(18*x) + 9*exp(27*x))/2!.

A076011 Fifth column of triangle A075504.

Original entry on oeis.org

1, 135, 11340, 765450, 45605511, 2511058725, 131122437930, 6597627438600, 323216347675221, 15525889656392115, 734898808902814920, 34399620992372494950, 1596504028634137480131, 73607593519321749694305

Offset: 0

Wolfdieter Lang, Oct 02 2002

The e.g.f. given below is Sum_{m=0..4} (A075513(5,m)*exp(9*(m+1)*x))/4!.

Michael De Vlieger, Table of n, a(n) for n = 0..604

Cf. A076010, A076012.

With[{m = 5}, Array[9^(# - m) StirlingS2[#, m] &, 14, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075504 *)

a(n) = A075504(n+5, 5) = (9^n)*S2(n+5, 5) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = Sum_{m=0..4} (A075513(5, m)*(9*(m+1))^n)/4!.
G.f.: 1/Product_{k=1..5} (1 - 9*k*x).
E.g.f.: (d^5/dx^5)(((exp(9*x)-1)/9)^5)/5! = (exp(9*x) - 64*exp(18*x) + 486*exp(27*x) - 1024*exp(36*x) + 625*exp(45*x))/4!.

cp's OEIS Frontend

A076009 Third column of triangle A075504.

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