A168622 Triangle T(n,k) with the coefficient [x^k] of the polynomial 7*(x+1)^n - 6*(x^n+1) in row n, column k. T(0,0)=1.

1, 1, 1, 1, 14, 1, 1, 21, 21, 1, 1, 28, 42, 28, 1, 1, 35, 70, 70, 35, 1, 1, 42, 105, 140, 105, 42, 1, 1, 49, 147, 245, 245, 147, 49, 1, 1, 56, 196, 392, 490, 392, 196, 56, 1, 1, 63, 252, 588, 882, 882, 588, 252, 63, 1, 1, 70, 315, 840, 1470, 1764, 1470, 840, 315, 70, 1

Offset

0,5

Comments

Row sums are 1, 2, 16, 44, 100, 212, 436, 884, 1780, 3572, 7156,.. apparently entries of A048489 multiplied by 2.

These plus forms generalize sequence A132047.

Links

Table of n, a(n) for n=0..65.

Example

1;
1, 1;
1, 14, 1;
1, 21, 21, 1;
1, 28, 42, 28, 1;
1, 35, 70, 70, 35, 1;
1, 42, 105, 140, 105, 42, 1;
1, 49, 147, 245, 245, 147, 49, 1;
1, 56, 196, 392, 490, 392, 196, 56, 1;
1, 63, 252, 588, 882, 882, 588, 252, 63, 1;
1, 70, 315, 840, 1470, 1764, 1470, 840, 315, 70, 1;

Mathematica

m = 3; p[x_, n_] := If[n == 0, 1, (2*m + 1)(x + 1)^n - 2*m*(x^n + 1)]
a = Table[CoefficientList[p[x, n], x], {n, 0, 10}];
Flatten[a]

Crossrefs

Cf. A168620, A131115.

Sequence in context: A040198 A040197 A040196 * A168293 A157633 A157278

Adjacent sequences: A168619 A168620 A168621 * A168623 A168624 A168625

Keyword

nonn,tabl,easy

Author

Roger L. Bagula and Gary W. Adamson, Dec 01 2009

Status

approved