|
Search: id:A092077
|
|
|
| A092077 |
|
Generalized Stirling2 array (8,2). |
|
+0
5
|
|
| 1, 56, 16, 1, 10192, 4928, 776, 48, 1, 3872960, 2477440, 575680, 63360, 3536, 96, 1, 2517424000, 1940556800, 572868800, 86163840, 7326880, 364800, 10480, 160, 1, 2497284608000, 2210343116800, 773352966400, 143430604800, 15836206400
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
The sequence of row lengths for this array is [1,3,5,7,9,11,...]=A005408(n-1), n>=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.
|
|
FORMULA
|
a(n, k)=(((-1)^k)/k!)*sum(((-1)^p)*binomial(k, p)*product(fallfac(p+6*(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=8, s=2.
Recursion: a(n, k)=sum(binomial(2, p)*fallfac(6*(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=8, s=2. fallfac(n, m) := A008279(n, m) (falling factorials triangle).
|
|
CROSSREFS
|
The generalized (k, 2)-Stirling2 arrays are, for k=2, ..., 7: A078739, A078740, A090438, A091534, A091746 and A091747.
Cf. A091546, A091552 (first, resp. second column). A091757 (row sums). A091758 (alternating row sums).
Sequence in context: A107676 A005932 A109737 this_sequence A033376 A003904 A008942
Adjacent sequences: A092074 A092075 A092076 this_sequence A092078 A092079 A092080
|
|
KEYWORD
|
nonn,easy,tabf
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 27 2004
|
|
|
Search completed in 0.002 seconds
|
