A091544 First column sequence of array A091746 ((6,2)-Stirling2).

1, 30, 2700, 491400, 150368400, 69470200800, 45155630520000, 39285398552400000, 44078217175792800000, 61973973349164676800000, 106719182107261573449600000, 220908706962031457040672000000

Offset

1,2

Comments

Also fifth column (m=4) 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.

Links

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

Formula

a(n)= 2^(n-1)*product((2*j+1)*(4*j+1), j=0..n-1), n>=1. From eq.12 of the Blasiak et al. reference with r=6, s=2, k=1.

a(n)= (2^(4*n-1))*risefac(1/4, n)*risefac(1/2, n), n>=1, with risefac(x, n) = Pochhammer(x, n).

a(n)= fac4(4*n-3)*fac4(4*n-2)/2, n>=1, with fac4(4*n-3)=A007696(n) and fac4(4*n-2)/2=A000407(n+1) (quartic- or 4-factorials).

E.g.f.: (hypergeom([1/4, 1/2], [], 16*x)-1)/2.

a(n)= A091746(n, 2), n>=1.

Crossrefs

Cf. A091535 (third column of A091543, first column of array A091534).

Sequence in context: A230612 A138916 A266041 * A230728 A352652 A108091

Adjacent sequences: A091541 A091542 A091543 * A091545 A091546 A091547

Keyword

nonn

Author

Wolfdieter Lang, Feb 13 2004

Status

approved