Carlitz, Leonard; Scoville, Richard Generalized Eulerian numbers: combinatorial applications. (English) Zbl 0276.05006 J. Reine Angew. Math. 265, 110-137 (1974). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 32 Documents MSC: 05A15 Exact enumeration problems, generating functions 05A10 Factorials, binomial coefficients, combinatorial functions 05A19 Combinatorial identities, bijective combinatorics 11B39 Fibonacci and Lucas numbers and polynomials and generalizations PDFBibTeX XMLCite \textit{L. Carlitz} and \textit{R. Scoville}, J. Reine Angew. Math. 265, 110--137 (1974; Zbl 0276.05006) Full Text: Crelle EuDML Online Encyclopedia of Integer Sequences: Triangle T(n,k) (n >= 1, 0 <= k <= floor((n-1)/2)) read by rows, where T(n,k) = (k+1)T(n-1,k) + (2n-4k)T(n-1,k-1). Triangle T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = x + 2.