A136255 Triangle T(n,k) read by rows: T(n,k) = (k+1) * A137276(n,k+1).

1, 0, 2, 1, 0, 3, 0, 0, 0, 4, -3, 0, -3, 0, 5, 0, -6, 0, -8, 0, 6, 5, 0, -6, 0, -15, 0, 7, 0, 16, 0, 0, 0, -24, 0, 8, -7, 0, 30, 0, 15, 0, -35, 0, 9, 0, -30, 0, 40, 0, 42, 0, -48, 0, 10, 9, 0, -75, 0, 35, 0, 84, 0, -63, 0, 11

Offset

1,3

Comments

Row sums are 1, 2, 4, 4, -1, -8, -9, 0, 12, 14, 1, ... with g.f. x*(1+3*x^2) / (x^2-x+1)^2.

Links

Table of n, a(n) for n=1..66.

Formula

T(n,k) = (k+1) * A137276(n,k+1) .

Example

Triangle starts:
{1},
{0, 2},
{1, 0, 3},
{0, 0, 0, 4},
{-3, 0, -3, 0, 5},
{0, -6, 0, -8, 0, 6},
{5, 0, -6, 0, -15, 0, 7},
{0, 16, 0, 0, 0, -24, 0, 8},
{-7, 0, 30, 0, 15, 0, -35, 0, 9},
{0, -30, 0, 40, 0,42, 0, -48, 0, 10},
{9, 0, -75, 0, 35, 0, 84, 0, -63, 0, 11},
...

Maple

B := proc(n, x) if n = 0 then 1; else add( (-1)^j*binomial(n-j, j)*(n-4*j)/(n-j)*x^(n-2*j), j=0..n/2) ; fi; end:
A136255 := proc(n, k) diff( B(n, x), x) ; coeftayl(%, x=0, k) ; end: seq( seq(A136255(n, k), k=0..n-1), n=1..15) ;

Mathematica

B[x, 0] = 1; B[x, 1] = x; B[x, 2] = 2 + x^2; B[x, 3] = x + x^3; B[x, 4] = -2 + x^4; B[x_, n_] := B[x, n] = x*B[x, n-1] - B[x, n-2]; P[x_, n_] := D[B[x, n + 1], x]; Flatten @ Table[CoefficientList[P[x, n], x], {n, 0, 10}]

Crossrefs

Cf. A138034, A135929, A135936, A137276, A137277, A137289.

Sequence in context: A266832 A307772 A225203 * A194812 A305320 A159813

Adjacent sequences: A136252 A136253 A136254 * A136256 A136257 A136258

Keyword

tabl,sign

Author

Roger L. Bagula, Mar 17 2008

Extensions

Edited by the Associate Editors of the OEIS, Aug 27 2009

Edited by and new name from Joerg Arndt, May 15 2016

Status

approved