A174952 Triangle t(n,m)= binomial(n+m-1,n-1) + binomial(2*n-m-1,n-1) -binomial(2*n-1,n-1) read by rows, 0<=m<=n.

1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -11, -15, -11, 1, 1, -51, -76, -76, -51, 1, 1, -204, -315, -350, -315, -204, 1, 1, -785, -1226, -1422, -1422, -1226, -785, 1, 1, -2995, -4683, -5523, -5775, -5523, -4683, -2995, 1, 1, -11431, -17830, -21142, -22528, -22528

Offset

0,12

Comments

Row sums are 1, 2, 3, 0, -35, -252, -1386, -6864, -32175, -145860, -646646,....

Links

Table of n, a(n) for n=0..50.

Formula

t(n,m) = t(n,n-m).

Example

1;
1, 1;
1, 1, 1;
1, -1, -1, 1;
1, -11, -15, -11, 1;
1, -51, -76, -76, -51, 1;
1 -204, -315, -350, -315, -204, 1;
1, -785, -1226, -1422, -1422, -1226, -785, 1;
1, -2995, -4683, -5523, -5775, -5523, -4683, -2995, 1;
1, -11431, -17830, -21142, -22528, -22528, -21142, -17830, -11431, 1;
1, -43748, -68013, -80718, -86658, -88374, -86658, -80718, -68013, -43748, 1;

Maple

A174952 := proc(n, m)
        binomial(n+m-1, n-1)+binomial(2*n-m-1, n-1) -binomial(2*n-1, n-1);
end proc: # R. J. Mathar, Jan 15 2013

Crossrefs

Cf. A158498, A059481

Sequence in context: A063964 A349224 A262721 * A209898 A371553 A139065

Adjacent sequences: A174949 A174950 A174951 * A174953 A174954 A174955

Keyword

sign,tabl,easy

Author

Roger L. Bagula, Apr 02 2010

Extensions

Definition corrected and deobfuscated. R. J. Mathar, Jan 15 2013

Status

approved