This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A091747 #9 Aug 28 2019 17:49:21 %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="/A091747/a091747.txt">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). %K A091747 nonn,easy,tabf %O A091747 1,2 %A A091747 _Wolfdieter Lang_, Feb 27 2004