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A091545 First column sequence of the array (7,2)-Stirling2 A091747. 1
1, 42, 5544, 1507968, 696681216, 489070213632, 485157651922944, 646229992361361408, 1112808046846264344576, 2405890997281623512973312, 6380422924790865556405223424, 20366309975932442856045473169408 (list; graph; refs; listen; history; internal format)
OFFSET

1,2

COMMENTS

Also sixth column (m=5) sequence 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.

FORMULA

a(n)= product((5*j+2)*(5*j+1), j=0..n-1)/2, n>=1. From eq.12 of the Blasiak et al. reference with r=7, s=2, k=1.

a(n)= (5^(2*n))*risefac(1/5, n)*risefac(2/5, n)/2, n>=1, with risefac(x, n) = Pochhammer(x, n).

a(n)= fac5(5*n-3)*fac5(5*n-4)/2, n>=1, with fac5(5*n-4)/2 = A034323(n) and fac5(5*n-3)= A008548(n) (5-factorials).

E.g.f.: (hypergeom([1/5, 2/5], [], 25*x)-1)/2.

a(n)=A091747(n, 2), n>=1.

CROSSREFS

Sequence in context: A053875 A048538 A102967 * A101630 A005791 A167668

Adjacent sequences:  A091542 A091543 A091544 * A091546 A091547 A091548

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 13 2004

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Last modified February 15 14:57 EST 2012. Contains 205823 sequences.