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A159856 Triangle read by rows: T(n,0) = n+1, T(n,k) = 2*T(n-1,k) - T(n-1,k-1), T(n,k) = 0 if k > n and if k < 0. 1
1, 2, -1, 3, -4, 1, 4, -11, 6, -1, 5, -26, 23, -8, 1, 6, -57, 72, -39, 10, -1, 7, -120, 201, -150, 59, -12, 1, 8, -247, 522, -501, 268, -83, 14, -1, 9, -502, 1291, -1524, 1037, 434, 111, -16, 1, 10, -1013, 3084, -4339, 3598, -1905, 656, -143, 18, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A Riordan array - see the Luzon references.

The second column is A000295 signed. - Michel Marcus, Feb 14 2014

LINKS

Table of n, a(n) for n=0..54.

Ana Luzón, Iterative Processes Related to Riordan Arrays: The Reciprocation and the Inversion of Power Series, arXiv:0907.2328 [math.CO]; Discrete Math., 310 (2010), 3607-3618.

Ana Luzón and Manuel A. Morón, Riordan matrices in the reciprocation of quadratic polynomials, Linear Algebra Appl. 430 (2009), no. 8-9, 22542270.

FORMULA

From R. J. Mathar, May 31 2009: (Start)

Sum_{k=0..n} T(n,k) = A080956(n).

Conjecture: Sum_{i=0..n} |T(n,k)| = A047926(n). (End)

T(n,k) = (-1)^k*Sum_{i=0..n-k} binomial(n+1,i+k+1)*binomial(i+k-1,k). - Vladimir Kruchinin, Nov 22 2016

G.f.: (1-2*x)/(1-x)^2/(1-2*x+y*x). - Vladimir Kruchinin, Nov 22 2016

EXAMPLE

Triangle begins

  1;

  2,   -1;

  3,   -4,    1;

  4,  -11,    6,   -1;

  5,  -26,   23,   -8,    1;

  6,  -57,   72,  -39,   10,   -1;

  7, -120,  201, -150,   59,  -12,    1;

  ...

PROG

(Maxima)

T(n, k):=coeff(taylor(1/(1-x)^2*(-x/(1-x))^k, x, 0, 15), x, n); /* Vladimir Kruchinin, Nov 22 2016 */

CROSSREFS

Cf. A181690.

Sequence in context: A133112 A247239 A198060 * A137649 A180915 A240783

Adjacent sequences:  A159853 A159854 A159855 * A159857 A159858 A159859

KEYWORD

easy,sign,tabl

AUTHOR

Philippe Deléham, Apr 24 2009

STATUS

approved

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Last modified March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)