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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-Fran├žois 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: A226441 A080246 A113413 * A136678 A110162 A199087

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 October 23 02:14 EDT 2019. Contains 328335 sequences. (Running on oeis4.)