A177276 Triangle T(n,k) with the coefficient [x^k] of the polynomial (1+x^2)^n + 2*n*x*(1+x^2)^(n-1) in row n, column k, 0<=k<=2n.

1, 1, 2, 1, 1, 4, 2, 4, 1, 1, 6, 3, 12, 3, 6, 1, 1, 8, 4, 24, 6, 24, 4, 8, 1, 1, 10, 5, 40, 10, 60, 10, 40, 5, 10, 1, 1, 12, 6, 60, 15, 120, 20, 120, 15, 60, 6, 12, 1, 1, 14, 7, 84, 21, 210, 35, 280, 35, 210, 21, 84, 7, 14, 1, 1, 16, 8, 112, 28, 336, 56, 560, 70, 560, 56, 336, 28, 112

Offset: 0

Author

Roger L. Bagula, May 06 2010

Keywords

• nonn
• tabf

Comments

Row sums are 1, 4, 12, 32, 80, 192, 448, 1024, 2304, 5120, 11264,..., A001787.

This is a generalization of A162246 to polynomials (1+x^2)^n + q*n*x*(1+x^2)^(n-1), here q=2.

Examples

			1;
1, 2, 1;
1, 4, 2, 4, 1;
1, 6, 3, 12, 3, 6, 1;
1, 8, 4, 24, 6, 24, 4, 8, 1;
1, 10, 5, 40, 10, 60, 10, 40, 5, 10, 1;
1, 12, 6, 60, 15, 120, 20, 120, 15, 60, 6, 12, 1;
1, 14, 7, 84, 21, 210, 35, 280, 35, 210, 21, 84, 7, 14, 1;
1, 16, 8, 112, 28, 336, 56, 560, 70, 560, 56, 336, 28, 112, 8, 16, 1;
1, 18, 9, 144, 36, 504, 84, 1008, 126, 1260, 126, 1008, 84, 504, 36, 144, 9, 18, 1;
1, 20, 10, 180, 45, 720, 120, 1680, 210, 2520, 252, 2520, 210, 1680, 120, 720, 45, 180, 10, 20, 1;
		

Crossrefs

Cf. A162246

Programs

Mathematica

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