A091747 Generalized Stirling2 array (7,2).
1, 42, 14, 1, 5544, 3192, 588, 42, 1, 1507968, 1165248, 321552, 41496, 2688, 84, 1, 696681216, 655966080, 232606080, 41497344, 4143552, 240240, 7980, 140, 1, 489070213632, 533531142144, 226306918656, 50249808000, 6575950080
Offset: 1
References
- P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.
- M. Schork, On the combinatorics of normal ordering bosonic operators and deforming it, J. Phys. A 36 (2003) 4651-4665.
Links
- W. Lang, First 6 rows.
Crossrefs
Formula
a(n, k)=(((-1)^k)/k!)*sum(((-1)^p)*binomial(k, p)*product(fallfac(p+5*(j-1), 2), j=1..n), p=2..k), n>=1, 2<=k<=2*n, else 0. From eq. (12) of the Blasiak et al. reference with r=7, s=2.
Recursion: a(n, k)=sum(binomial(2, p)*fallfac(5*(n-1)+k-p, 2-p)*a(n-1, k-p), p=0..2), n>=2, 2<=k<=2*n, a(1, 2)=1, else 0. Rewritten from eq.(19) of the Schork reference with r=7, s=2. fallfac(n, m) := A008279(n, m) (falling factorials triangle).
Comments