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 A287696 Triangle read by rows, T(n,k) = (n!)^3 * [x^k] [z^n] hypergeom([], [1, 1], z)^x for n>=0, 0<=k<=n. 2
 1, 0, 1, 0, -3, 4, 0, 46, -81, 36, 0, -1899, 3916, -2592, 576, 0, 163476, -375375, 305500, -108000, 14400, 0, -25333590, 63002191, -58725000, 26370000, -5832000, 518400, 0, 6412369860, -16976577828, 17470973569, -9168390000, 2636298000, -400075200, 25401600 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The polynomials Sum_{k=0..n} T(n,k) x^k generate the columns of A287698. LINKS Table of n, a(n) for n=0..35. FORMULA Sum_{k=0..n} T(n,k) = A000012(n). Sum_{k=0..n} abs(T(n,k)) = A212856(n) = A212855_row(3). EXAMPLE 0: [1] 1: [0, 1] 2: [0, -3, 4] 3: [0, 46, -81, 36] 4: [0, -1899, 3916, -2592, 576] 5: [0, 163476, -375375, 305500, -108000, 14400] 6: [0, -25333590, 63002191, -58725000, 26370000, -5832000, 518400] MAPLE A287696_row := proc(n) local k; hypergeom([], [1, 1], z); series(%^x, z=0, n+1): n!^3*coeff(%, z, n); seq(coeff(%, x, k), k=0..n) end: for n from 0 to 8 do A287696_row(n) od; A287696_poly := proc(n) local k, x; hypergeom([], [1, 1], z); series(%^x, z=0, n+1): unapply(n!^3*coeff(%, z, n), x); end: for n from 0 to 7 do A287696_poly(n) od; MATHEMATICA T[n_, k_] := (n!)^3 SeriesCoefficient[HypergeometricPFQ[{}, {1, 1}, z]^x, {x, 0, k}, {z, 0, n}]; Table[T[n, k], {n, 0, 7}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 13 2017 *) CROSSREFS T(n,n) = A001044(n). Cf. A212856, A212855, A287314, A287698. Sequence in context: A322278 A102222 A171657 * A366465 A084301 A195788 Adjacent sequences: A287693 A287694 A287695 * A287697 A287698 A287699 KEYWORD sign,tabl AUTHOR Peter Luschny, May 30 2017 STATUS approved

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Last modified May 23 20:34 EDT 2024. Contains 372765 sequences. (Running on oeis4.)