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A091546 First column of the array A092077 ((8,2)-Stirling2). 1
1, 56, 10192, 3872960, 2517424000, 2497284608000, 3511182158848000, 6643156644540416000, 16275733779124019200000, 50129260039701979136000000, 189588861470152885092352000000, 863766852858016544480755712000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also seventh column (m=6) of triangle A091543.

REFERENCES

P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.

LINKS

Table of n, a(n) for n=1..12.

FORMULA

a(n)= (2^(n-1))*product((3*j+1)*(6*j+1), j=0..n-1), n>=1. From eq.12 of the Blasiak et al. reference with r=8, s=2, k=1.

a(n)= (6^(2*n))*risefac(1/6, n)*risefac(1/3, n)/2, n>=1, with risefac(x, n) = Pochhammer(x, n).

a(n)= fac6(6*n-5)*fac6(6*n-4)/2, n>=1, with fac6(6*n-5) = A008542(n) and fac6(6*n-4)/2 = A034689(n)= (2^(n-1))*A007559(n), (6-factorials).

CROSSREFS

Sequence in context: A202922 A034204 A275921 * A059989 A352602 A184125

Adjacent sequences: A091543 A091544 A091545 * A091547 A091548 A091549

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Feb 13 2004

STATUS

approved

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Last modified February 4 10:00 EST 2023. Contains 360046 sequences. (Running on oeis4.)