Search: id:A091747
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%I A091747
%S A091747 1,42,14,1,5544,3192,588,42,1,1507968,1165248,321552,41496,2688,84,1,
%T A091747 696681216,655966080,232606080,41497344,4143552,240240,7980,140,1,
%U A091747 489070213632,533531142144,226306918656,50249808000,6575950080
%N A091747 Generalized Stirling2 array (7,2).
%C A091747 The sequence of row lengths for this array is [1,3,5,7,9,11,...]=A005408(n-1), 
               n>=1.
%D A091747 P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal 
               ordering problem, Phys. Lett. A 309 (2003) 198-205.
%D A091747 M. Schork, On the combinatorics of normal ordering bosonic operators 
               and deforming it, J. Phys. A 36 (2003) 4651-4665.
%H A091747 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A091747.text">
               First 6 rows</a>.
%F A091747 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.
%F A091747 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).
%Y A091747 Cf. A078740 (3, 2)-Stirling2, A090438 (4, 2)-Stirling2, A091534 (5, 2)-Stirling2, 
               A091746 (6, 2)-Stirling2.
%Y A091747 Cf. A091545 (first column).
%Y A091747 Cf. A091749 (row sums), A091751 (alternating row sums).
%Y A091747 Sequence in context: A023932 A022074 A037938 this_sequence A030434 A033362 
               A033976
%Y A091747 Adjacent sequences: A091744 A091745 A091746 this_sequence A091748 A091749 
               A091750
%K A091747 nonn,easy,tabf
%O A091747 1,2
%A A091747 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Feb 27 2004

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