A075923 -id:A075923 - cp's OEIS frontend

A075924 Fifth column of triangle A075502.

1, 105, 6860, 360150, 16689351, 714717675, 29027537770, 1135995214200, 43285014073301, 1617172212901245, 59536438207963080, 2167526889938878650, 78241359077417918851, 2805721220626405336815, 100098458195602131838790

Offset: 0

Wolfdieter Lang, Oct 02 2002

The e.g.f. given below is Sum_{m=0..4} A075513(5,m)*exp(7*(m+1)*x)/4!.

Cf. A075923, A075925.

a(n) = A075502(n+5, 5) = (7^n)*S2(n+5, 5) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = Sum_{m=0..4} A075513(5, m)*((m+1)*7)^n/4!.
G.f.: 1/Product_{k=1..5} (1 - 7*k*x).
E.g.f.: (d^5/dx^5)(((exp(7*x)-1)/7)^5)/5! = (exp(7*x) - 64*exp(14*x) + 486*exp(21*x) - 1024*exp(28*x) + 625*exp(35*x))/4!.

A075922 Third column of triangle A075502.

Original entry on oeis.org

1, 42, 1225, 30870, 722701, 16235562, 355888225, 7683656190, 164302593301, 3491636199282, 73902587019625, 1560051480424710, 32874455072382301, 691950889177526202, 14553192008156093425, 305928163614832076430

Offset: 0

Wolfdieter Lang, Oct 02 2002

The e.g.f. given below is Sum_{m=0..2} A075513(3,m)*exp(7*(m+1)*x)/2!.

Cf. A075921, A075923.

a(n) = A075502(n+3, 3) = (7^n)*S2(n+3, 3) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = (7^n - 8*14^n + 9*21^n)/2.
G.f.: 1/Product_{k=1..3} (1 - 7*k*x).
E.g.f.: (d^3/dx^3)(((exp(7*x)-1)/7)^3)/3! = (exp(7*x) - 8*exp(14*x) + 9*exp(21*x))/2!.

cp's OEIS Frontend

A075924 Fifth column of triangle A075502.

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