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 A257635 Triangle with n-th row polynomial equal to Product_{k = 1..n} (x + n + k). 2
 1, 2, 1, 12, 7, 1, 120, 74, 15, 1, 1680, 1066, 251, 26, 1, 30240, 19524, 5000, 635, 40, 1, 665280, 434568, 117454, 16815, 1345, 57, 1, 17297280, 11393808, 3197348, 495544, 45815, 2527, 77, 1, 518918400, 343976400, 99236556, 16275700, 1659889, 107800, 4354, 100, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The row polynomials are a Sheffer sequence. For the associated polynomial sequence of binomial type see A038455. LINKS R. Sprugnoli, An Introduction to Mathematical Methods in Combinatorics, Section 5.6 CreateSpace Independent Publishing Platform 2006, ISBN-13: 978-1502925244 Wikipedia, Sheffer sequence FORMULA E.g.f. A(x,t) = B(t)*C(t)^x = 1 + (2 + x)*t + (3 + x)*(4 + x)*t^2/2! + (4 + x)*(5 + x)*(6 + x)*t^3/3! + ..., where B(t) = 1/sqrt(1 - 4*t) is the o.g.f. for A000984 and C(t) = (1 - sqrt(1 - 4*t))/(2*t) is the o.g.f. for A000108. n-th row polynomial: n!*binomial(2*n + x,n). EXAMPLE Triangle begins 1, 2, 1, 12, 7, 1, 120, 74, 15, 1, 1680, 1066, 251, 26, 1, 30240, 19524, 5000, 635, 40, 1, 665280, 434568, 117454, 16815, 1345, 57, 1, ... MAPLE seq(seq(coeff(product(n + x + k, k = 1 .. n), x, i), i = 0..n), n = 0..8); CROSSREFS A001813 (column 0), A005449 (first subdiagonal), A098118 (column 1). Cf. A000108, A000984, A038455, A092932. Sequence in context: A132875 A050139 A010255 * A085752 A074966 A128413 Adjacent sequences:  A257632 A257633 A257634 * A257636 A257637 A257638 KEYWORD nonn,tabl,easy AUTHOR Peter Bala, Nov 05 2015 STATUS approved

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Last modified October 21 20:44 EDT 2019. Contains 328315 sequences. (Running on oeis4.)