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

0,3

Comments

Row sums are in A001792.

Links

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

Example

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;

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}]

Crossrefs

Cf. A162246

Sequence in context: A213670 A116609 A124846 * A099512 A127096 A130541

Adjacent sequences: A177372 A177373 A177374 * A177376 A177377 A177378

Keyword

nonn,tabl

Author

Roger L. Bagula, May 07 2010

Status

approved