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A075512 Seventh column of triangle A075497. 3
1, 56, 1848, 47040, 1023792, 20076672, 365787136, 6314147840, 104637781248, 1680323893248, 26325099300864, 404403166003200, 6115019304300544, 91287994741981184, 1348582723009708032 (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(2*(m+1)*x)/6!.

LINKS

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

FORMULA

a(n) = A075497(n+7, 7) = (2^n)*S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..6} A075513(7, m)*((m+1)*2)^n/6!.

G.f.: 1/Product_{k=1..7} (1 - 2*k*x).

E.g.f.: (d^7/dx^7)(((exp(2*x)-1)/2)^7)/7! = (exp(2*x) - 384*exp(4*x) + 10935*exp(6*x) - 81920*exp(8*x) + 234375*exp(10*x) - 279936*exp(12*x) + 117649*exp(14*x))/6!.

CROSSREFS

Cf. A075511.

Sequence in context: A050989 A333067 A140406 * A223958 A000504 A130646

Adjacent sequences:  A075509 A075510 A075511 * A075513 A075514 A075515

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 02 2002

STATUS

approved

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Last modified April 8 14:52 EDT 2020. Contains 333314 sequences. (Running on oeis4.)