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A075909 Sixth column of triangle A075499. 1
1, 84, 4256, 169344, 5843712, 183794688, 5421678592, 152720375808, 4157366140928, 110282217357312, 2867778350481408, 73424436820180992, 1857023919127527424, 46511918954689069056, 1155904251854380335104 (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(4*(m+1)*x)/5!.

LINKS

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

FORMULA

a(n) = A075499(n+6, 6) = (4^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..5} A075513(6, m)*((m+1)*4)^n/5!.

G.f.: 1/Product_{k=1..6} (1 - 4*k*x).

E.g.f.: (d^6/dx^6)(((exp(4*x)-1)/4)^6)/6! = (-exp(4*x) + 160*exp(8*x) - 2430*exp(12*x) + 10240*exp(16*x) - 15625*exp(20*x) + 7776*exp(24*x))/5!.

CROSSREFS

Cf. A075908, A075910.

Sequence in context: A143402 A004379 A075906 * A132052 A273438 A097840

Adjacent sequences:  A075906 A075907 A075908 * A075910 A075911 A075912

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 02 2002

STATUS

approved

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Last modified February 21 17:15 EST 2020. Contains 332100 sequences. (Running on oeis4.)