A076012 -id:A076012 - cp's OEIS frontend

A076013 Seventh column of triangle A075504.

1, 252, 37422, 4286520, 419818707, 37047106404, 3037410645984, 235940417032320, 17594974122819093, 1271468563282273356, 89638618747098243186, 6196581962116572990600, 421646012618644954061559

Offset: 0

Wolfdieter Lang, Oct 02 2002

The e.g.f. given below is Sum_{m=0..6} (A075513(7,m)*exp(9*(m+1)*x))/6!.

Michael De Vlieger, Table of n, a(n) for n = 0..554

Cf. A075504, A075513, A076012.

With[{m = 7}, Array[9^(# - m) StirlingS2[#, m] &, 13, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075504 *)

a(n) = A075504(n+7, 7) = (9^n)*S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = Sum_{m=0..6} (A075513(7, m)*((m+1)*9)^n)/6!.
G.f.: 1/Product_{k=1..7} (1 - 9*k*x).
E.g.f.: (d^7/dx^7)(((exp(9*x)-1)/9)^7)/7! = (exp(9*x) - 384*exp(18*x) + 10935*exp(27*x) - 81920*exp(36*x) + 234375*exp(45*x) - 279936*exp(54*x) + 117649*exp(63*x))/6!.

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

A076013 Seventh column of triangle A075504.

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