A132815 A007318^(-1) * A132814.

1, -1, 2, 1, -2, 3, -1, 0, 0, 4, 1, 4, -12, 8, 5, -1, -10, 30, -40, 25, 6, 1, 18, -45, 60, -75, 54, 7, -1, -28, 42, 0, 0, -84, 98, 8, 1, 40, 0, -224, 420, -336, 0, 160, 9, -1, -54, -108, 672, -1260, 1512, -1176, 288, 243, 10

Offset

0,3

Comments

Row sums = A001405: (1, 1, 2, 3, 6, 10, 10, ...).

Links

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

Formula

Inverse binomial transform of A132814.

Example

First few rows of the triangle:
   1;
  -1,   2;
   1,  -2,   3;
  -1,   0,   0,    4;
   1,   4, -12,    8,   5;
  -1, -10,  30, -240,  25,  6;
   1,  18, -45,   60, -75, 54, 7;
  ...

Prog

(PARI) tabl(nn) = {t007318 = matrix(nn, nn, n, k, binomial(n-1, k-1)); t132813 = matrix(nn, nn, n, k, binomial(n-1, k-1)*binomial(n, k-1)); t132814 = t007318^(-1)*t132813; t132815 = t007318^(-1)*t132814; for (n=1, nn, for (k=1, n, print1(t132815[n, k], ", "); ); ); } \\ Michel Marcus, Feb 12 2014

Crossrefs

Cf. A001405, A007318, A132814.

Sequence in context: A317441 A249777 A289065 * A167684 A094646 A124448

Adjacent sequences: A132812 A132813 A132814 * A132816 A132817 A132818

Keyword

tabl,easy,sign

Author

Gary W. Adamson, Sep 01 2007

Extensions

Typo corrected by Travis Hoppe, Apr 24 2008

T(5, 1) corrected by Michel Marcus, Feb 12 2014

Status

approved