A075917 -id:A075917 - cp's OEIS frontend

A075916 Third column of triangle A075501.

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

Offset: 0

Wolfdieter Lang, Oct 02 2002

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

Cf. A016175, A075917.

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!.

A075918 Fifth column of triangle A075501.

Original entry on oeis.org

1, 90, 5040, 226800, 9008496, 330674400, 11511434880, 386143718400, 12611398415616, 403864019919360, 12744269679697920, 397694704355020800, 12304809943691636736, 378212825199337758720, 11565710925825703772160

Offset: 0

Wolfdieter Lang, Oct 02 2002

The e.g.f. given below is Sum_{m=0..4} A075513(5,m)*exp(6*(m+1)*x)/4!.

Cf. A075917, A075919.

a(n) = A075501(n+5, 5) = (6^n)*S2(n+5, 5) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = Sum_{m=0..4} A075513(5, m)*((m+1)*6)^n/4!.
G.f.: 1/Product_{k=1..5} (1 - 6*k*x).
E.g.f.: (d^5/dx^5)(((exp(6*x)-1)/6)^5)/5! = (exp(6*x) - 64*exp(12*x) + 486*exp(18*x) - 1024*exp(24*x) + 625*exp(30*x))/4!.

cp's OEIS Frontend

A075916 Third column of triangle A075501.

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