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 A125694 Riordan array ((1+3x-sqrt(1+2x+9x^2))/(2x),(1+3x-sqrt(1+2x+9x^2))/2). 4
 1, -2, 1, 2, -4, 1, 2, 8, -6, 1, -10, -4, 18, -8, 1, 6, -24, -26, 32, -10, 1, 42, 60, -18, -72, 50, -12, 1, -102, 24, 162, 48, -150, 72, -14, 1, -82, -388, -214, 248, 230, -268, 98, -16, 1, 782, 536, -546, -800, 158, 600, -434, 128, -18, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First column is A125695. Row sums are A091593. Inverse of A125693. LINKS Table of n, a(n) for n=0..54. FORMULA T(n-1,k-1) = (k/n)*sum_{i=0..n-k} binomial(n,n-k-i) *(-3)^(n-k-i) *binomial(i+n-1,n-1). - Vladimir Kruchinin, Feb 12 2011 T(n, k) = (-3)^(n-k)*C(n,k)*hypergeometric([k-n, n+1], [k+2], 1/3). - Peter Luschny, Sep 17 2014 EXAMPLE Triangle begins 1, -2, 1, 2, -4, 1, 2, 8, -6, 1, -10, -4, 18, -8, 1, 6, -24, -26, 32, -10, 1, 42, 60, -18, -72, 50, -12, 1 MATHEMATICA m = 9; T[0, 0] = 1; T[1, 0] = 2; T[1, 1] = 1; T[n_, k_] /; 0 <= k <= n := T[n, k] = 3 T[n - 1, k] + T[n - 1, k - 1] - T[n - 2, k - 1]; T[_, _] = 0; M = Table[T[n, k], {n, 0, m}, {k, 0, m}] // Inverse; A[n_, k_] := M[[n + 1, k + 1]]; Table[A[n, k], {n, 0, m}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 13 2019 *) PROG (Sage) A125694 = lambda n, k : (-3)^(n-k)*binomial(n, k)*hypergeometric([k-n, n+1], [k+2], 1/3) for n in (0..6): [round(A125694(n, k).n(100)) for k in (0..n)] # Peter Luschny, Sep 17 2014 CROSSREFS Sequence in context: A080246 A113413 A333571 * A136678 A110162 A350228 Adjacent sequences: A125691 A125692 A125693 * A125695 A125696 A125697 KEYWORD easy,sign,tabl AUTHOR Paul Barry, Nov 30 2006 STATUS approved

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Last modified June 2 15:42 EDT 2023. Contains 363098 sequences. (Running on oeis4.)
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