A177375 Triangle t(n,k): the coefficient [x^k] of the series (1+x)^n + 2*n*x*(1+x)^(n-2), in row n, column k.

1, 1, 3, 1, 6, 1, 1, 9, 9, 1, 1, 12, 22, 12, 1, 1, 15, 40, 40, 15, 1, 1, 18, 63, 92, 63, 18, 1, 1, 21, 91, 175, 175, 91, 21, 1, 1, 24, 124, 296, 390, 296, 124, 24, 1, 1, 27, 162, 462, 756, 756, 462, 162, 27, 1, 1, 30, 205, 680, 1330, 1652, 1330, 680, 205, 30, 1

Offset: 0

Author

Roger L. Bagula, May 07 2010

Keywords

• nonn
• tabl

Comments

Row sums are in A001792.

Examples

			1;
1, 3;
1, 6, 1;
1, 9, 9, 1;
1, 12, 22, 12, 1;
1, 15, 40, 40, 15, 1;
1, 18, 63, 92, 63, 18, 1;
1, 21, 91, 175, 175, 91, 21, 1;
1, 24, 124, 296, 390, 296, 124, 24, 1;
1, 27, 162, 462, 756, 756, 462, 162, 27, 1;
1, 30, 205, 680, 1330, 1652, 1330, 680, 205, 30, 1;
		

Crossrefs

Cf. A162246

Programs

Maple

A177375 := proc(n,k)
    (1+x)^n+2*n*x*(1+x)^(n-2) ;
    coeftayl(%,x=0,k)
end proc: # R. J. Mathar, May 19 2013

Mathematica

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