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A075906 Seventh column of triangle A075498. 3
1, 84, 4158, 158760, 5182947, 152457228, 4166544096, 107883135360, 2681751885813, 64597295294532, 1518037879508514, 34979886546859800, 793401360863472999, 17766424516726033596, 393690756719422620612 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The e.g.f. given below is Sum_{m=0..6} A075513(7,m)*exp(3*(m+1)*x)/6!.

LINKS

Table of n, a(n) for n=0..14.

FORMULA

a(n) = A075498(n+7, 7) = (3^n)*S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..6} A075513(7, m)*((m+1)*3)^n/6!.

G.f.: 1/Product_{k=1..7} (1 - 3*k*x).

E.g.f.: (d^7/dx^7)(((exp(3*x)-1)/3)^7)/7! = (exp(3*x) - 384*exp(6*x) + 10935*exp(9*x) - 81920*exp(12*x) + 234375*exp(15*x) - 279936*exp(18*x) + 117649*exp(21*x))/6!.

CROSSREFS

Cf. A075516.

Sequence in context: A223959 A143402 A004379 * A075909 A132052 A273438

Adjacent sequences:  A075903 A075904 A075905 * A075907 A075908 A075909

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 02 2002

STATUS

approved

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Last modified March 28 17:28 EDT 2020. Contains 333090 sequences. (Running on oeis4.)