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%I A132056 #25 Aug 28 2019 15:44:17
%S A132056 1,8,1,120,24,1,2640,672,48,1,76560,22800,2160,80,1,2756160,920160,
%T A132056 104880,5280,120,1,118514880,43243200,5639760,347760,10920,168,1,
%U A132056 5925744000,2323918080,336510720,24071040,937440,20160,224,1
%N A132056 Triangle read by rows, the Bell transform of Product_{k=0..n} 7*k+1 without column 0.
%C A132056 Previous name was: Triangle of numbers related to triangle A132057; generalization of Stirling numbers of second kind A008277, Lah-numbers A008297, ...
%C A132056 a(n,m) enumerates unordered n-vertex m-forests composed of m plane increasing 8-ary trees. See the F. Bergeron et al. reference, especially Table 1, first row, for the e.g.f. for m=1.
%C A132056 a(n,m) := S2(8; n,m) is the eighth triangle of numbers in the sequence S2(k;n,m), k=1..7: A008277 (unsigned Stirling 2nd kind), A008297 (unsigned Lah), A035342, A035469, A049029, A049385, A092082, respectively. a(n,1)=A045754(n), n>=1.
%H A132056 F. Bergeron, Ph. Flajolet and B. Salvy, Varieties of Increasing Trees, Lecture Notes in Computer Science vol. 581, ed. J.-C. Raoult, Springer 1992, pp. 24-48.
%H A132056 P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.
%H A132056 P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, arXiv:quant-ph/0402027, 2004.
%H A132056 W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
%H A132056 M. Janjic, Some classes of numbers and derivatives, JIS 12 (2009) 09.8.3
%H A132056 W. Lang, First 10 rows.
%F A132056 a(n, m) = n!*A132057(n, m)/(m!*7^(n-m)); a(n+1, m) = (7*n+m)*a(n, m)+ a(n, m-1), n >= m >= 1; a(n, m) := 0, n