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A075919 Sixth column of triangle A075501. 2
1, 126, 9576, 571536, 29583792, 1395690912, 61756307712, 2609370796032, 106548747072768, 4239618914539008, 165370550603102208, 6351034526066700288, 240942052882092847104, 9052126728954680254464 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) = A075501(n+6, 6) = (6^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..5} A075513(6, m)*((m+1)*6)^n/5!.

G.f.: 1/Product_{k=1..6} (1 - 6*k*x).

E.g.f.: (d^6/dx^6)(((exp(6*x)-1)/6)^6)/6! = (-exp(6*x) + 160*exp(12*x) - 2430*exp(18*x) + 10240*exp(24*x) - 15625*exp(30*x) + 7776*exp(36*x))/5!.

CROSSREFS

Cf. A075918, A075920.

Sequence in context: A202652 A278624 A156931 * A278306 A180885 A241172

Adjacent sequences:  A075916 A075917 A075918 * A075920 A075921 A075922

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 02 2002

STATUS

approved

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Last modified July 4 20:49 EDT 2022. Contains 355086 sequences. (Running on oeis4.)