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A136659 Unsigned third column (k=2) of triangle A136656 divided by 4. 3
1, 9, 75, 660, 6300, 65520, 740880, 9072000, 119750400, 1696464000, 25686460800, 414096883200, 7083236160000, 128152088064000, 2445351068160000, 49084865077248000, 1033983353475072000, 22808456326656000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also unsigned second column of triangle A136657 divided by 2.

REFERENCES

Ch. A. Charalambides, Enumerative Combinatorics, Chapman & Hall/CRC, Boca Raton, Florida, 2002, Table 8.3, p. 311, with s=-2, k=2 column/4.

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n)= |A136656(n+2,2)|/4, n>=0.

E.g.f.(derived from the one given for the column k=2 under A136656): (2+6*x-3*x^2)/(2*(1-x)^6).

a(n)=(n+4)!/2 * sum((k+1)!/(k+4)!,k=1..n), with offset 1 [From Gary Detlefs, Jul 27 2010]

a(n)= 1/48 * (n+8)*(n+1)*(n+3)! [From Gary Detlefs, Aug 03 2010]

CROSSREFS

Cf. A001710 (1/2 of unsigned k=1 column of A136657). A136660 (k=3 column divided by 8).

Sequence in context: A190983 A254664 A223204 * A231592 A126965 A066222

Adjacent sequences:  A136656 A136657 A136658 * A136660 A136661 A136662

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang Feb 22 2008

STATUS

approved

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Last modified April 5 14:56 EDT 2020. Contains 333245 sequences. (Running on oeis4.)