A065432 Triangle related to Catalan triangle: recurrence related to A033877 (Schroeder numbers).

1, 1, -1, 1, -2, 0, 1, -3, 1, 1, 1, -4, 3, 2, 0, 1, -5, 6, 2, -2, -2, 1, -6, 10, 0, -6, -4, 0, 1, -7, 15, -5, -11, -3, 5, 5, 1, -8, 21, -14, -15, 4, 15, 10, 0, 1, -9, 28, -28, -15, 19, 26, 6, -14, -14, 1, -10, 36, -48, -7, 42, 30, -16, -42, -28, 0, 1, -11, 45, -75, 14, 70, 16, -60, -70, -14, 42, 42, 1, -12, 55, -110, 54, 96, -28, -120, -70, 56, 126, 84, 0

Offset

0,5

Comments

Sums of odd rows are 0, of even rows are the Catalan numbers (A000108) with alternating signs. Row sums of unsigned version give A065441.

Links

Table of n, a(n) for n=0..90.

Example

Triangle starts:
[0] 1;
[1] 1, -1;
[2] 1, -2,  0;
[3] 1, -3,  1,   1;
[4] 1, -4,  3,   2,   0;
[5] 1, -5,  6,   2,  -2, -2;
[6] 1, -6, 10,   0,  -6, -4,  0;
[7] 1, -7, 15,  -5, -11, -3,  5,  5;
[8] 1, -8, 21, -14, -15,  4, 15, 10,   0;
[9] 1, -9, 28, -28, -15, 19, 26,  6, -14, -14.

Mathematica

a[0, 0] := 1; a[n_, k_] := 0/; (k > n||n < 0||k < 0); a[n_, k_] := a[n, k] = a[n, k-1]-2a[n-1, k-1]+a[n-1, k]; Table[a[n, k], {n, 0, 16}, {k, 0, n}]

Crossrefs

Sequence in context: A261209 A340006 A093555 * A094184 A078805 A122837

Adjacent sequences: A065429 A065430 A065431 * A065433 A065434 A065435

Keyword

sign,tabl

Author

Wouter Meeussen, Nov 16 2001

Extensions

More terms from Sean A. Irvine, Sep 03 2023

Status

approved