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 A180401 Stirling-like sequence obtained from bipartite 0-1 tableaux. 0
 1, 0, 1, 0, 1, 1, 0, 4, 4, 1, 0, 36, 33, 10, 1, 0, 576, 480, 148, 20, 1, 0, 14400, 10960, 3281, 483, 35, 1, 0, 518400, 362880, 103824, 15552, 1288, 56, 1, 0, 25401600, 16465680, 4479336, 663633, 57916, 2982, 84, 1, 0, 1625702400, 981872640, 253732096, 36690816, 3252624, 181312, 6216, 120, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Gives the number of ways to construct pairs of permutations of an n-element set into k cycles such that the sum of the minima of the i-th cycle of the first permutation and the (k-i+1)-th cycle of the second permutation is n+1. LINKS K. J. M. Gonzales, Enumeration of Restricted Permutation Pairs and Partitions Pairs via 0-1 Tableaux, arXiv:1008.4192 [math.CO], 2010-2014. A. de Medicis and P. Leroux, Generalized Stirling Numbers, Convolution Formulae and p,q-Analogues, Can. J. Math. 47 (1995), 474-499. FORMULA G.f.: sum_{all r=>0} C(n,k) x^r = prod_{all v+w=n,0<=v,w<=n-1} (x+vw) Symm. f: C(n,k)=sum_{all 0 <=i_1k){ Atab<-combn(1:n-1, n-k) Btab<-n-1-Atab+beta Atab<-Atab+alpha px<-NULL for(i in 1:ncol(Atab)){ partial<-NULL for(j in 1:nrow(Atab)){ partial<-c(partial, (v(seq.a[Atab[j, i]+1])*w(seq.b[Btab[j, i]+1]))) } # for(j in 1:nrow(Atab)) px<-c(px, prod(partial)) }# for(i in 1:ncol(Atab)) } # if(n>k) if(n>k) x<-sum(px) if(n==k) x=1 if(n

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Last modified June 4 01:51 EDT 2020. Contains 334811 sequences. (Running on oeis4.)