A075919 -id:A075919 - cp's OEIS frontend

A075918 Fifth column of triangle A075501.

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!.

A075920 Seventh column of triangle A075501.

Original entry on oeis.org

1, 168, 16632, 1270080, 82927152, 4878631296, 266658822144, 13809041326080, 686528482768128, 33073815190800384, 1554470788616718336, 71638807647968870400, 3249771974096785403904, 145542549641019667218432

Offset: 0

Wolfdieter Lang, Oct 02 2002

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

Cf. A075919.

a(n) = A075501(n+7, 7) = (6^n)S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = Sum_{m=0..6} A075513(7, m)*((m+1)*6)^n/6!.
G.f.: 1/Product_{k=1..7} (1 - 6*k*x).
E.g.f.: (d^7/dx^7)(((exp(6*x)-1)/6)^7)/7! = (exp(6*x) - 384*exp(12*x) + 10935*exp(18*x) - 81920*exp(24*x) + 234375*exp(30x) - 279936*exp(36*x) + 117649*exp(42*x))/6!.

cp's OEIS Frontend

A075918 Fifth column of triangle A075501.

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