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 A179927 Triangle of centered orthotopic numbers 4
 1, 1, 2, 1, 3, 2, 1, 5, 5, 2, 1, 9, 13, 7, 2, 1, 17, 35, 25, 9, 2, 1, 33, 97, 91, 41, 11, 2, 1, 65, 275, 337, 189, 61, 13, 2, 1, 129, 793, 1267, 881, 341, 85, 15, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS T(n, k) = [x^k] series[ H(n - k, x) ] Here H(n,x) = E(n,x)*(1+x)/(1-x)^(n+1) where E(n,x) are the Eulerian polynomials, E(0,x) = 1 and E(n,x) = sum_{k=0^{n-1}} W_{n,k} x^k for n > 0. W_{n,k} as in DLMF Table 26.14.1. LINKS Peter Luschny, Figurate number - a very short introduction EXAMPLE 1 1, 2 1, 3, 2 1, 5, 5, 2 1, 9, 13, 7, 2 1, 17, 35, 25, 9, 2 1, 33, 97, 91, 41, 11, 2 MAPLE E := (n, x) -> `if`(n=0, 1, x*(1-x)*diff(E(n-1, x), x)+E(n-1, x)*(1+(n-1)*x)); H := (n, x) -> E(n, x)*(1+x)/(1-x)^(n+1); A179927 := (n, k) -> coeff(series(H(n-k, x), x, 18), x, k); seq(print(seq(A179927(n, k), k=0..n)), n=0..6); MATHEMATICA e[0, _] = 1; e[n_, x_] := e[n, x] = x(1-x) D[e[n-1, x], x] + e[n-1, x] (1 + (n-1)x); h[n_, x_] := e[n, x] (1+x)/(1-x)^(n+1); T[n_, k_] := SeriesCoefficient[h[n-k, x], {x, 0, k}]; Table[T[n, k], {n, 0, 8}, {k, 0, n}] (* Jean-François Alcover, Jun 17 2019, from Maple *) CROSSREFS Cf. Row sums in A179928, triangle of orthotopic numbers is A009998. Sequence in context: A038497 A091355 A131245 * A104446 A131345 A134423 Adjacent sequences:  A179924 A179925 A179926 * A179928 A179929 A179930 KEYWORD nonn,tabl AUTHOR Peter Luschny, Aug 02 2010 STATUS approved

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Last modified October 22 05:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)