A146766 Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 2)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].

1, 1, 1, 1, 6, 1, 1, 15, 15, 1, 1, 36, 54, 36, 1, 1, 85, 170, 170, 85, 1, 1, 198, 495, 660, 495, 198, 1, 1, 455, 1365, 2275, 2275, 1365, 455, 1, 1, 1032, 3612, 7224, 9030, 7224, 3612, 1032, 1, 1, 2313, 9252, 21588, 32382, 32382, 21588, 9252, 2313, 1, 1, 5130, 23085

Offset

0,5

Comments

Row sums are: {1, 2, 8, 32, 128, 512, 2048, 8192, 32768, 131072, 524288}.

Links

Table of n, a(n) for n=0..57.

Example

Triangle begins:
{1},
{1, 1},
{1, 6, 1},
{1, 15, 15, 1},
{1, 36, 54, 36, 1},
{1, 85, 170, 170, 85, 1},
{1, 198, 495, 660, 495, 198, 1},
{1, 455, 1365, 2275, 2275, 1365, 455, 1},
{1, 1032, 3612, 7224, 9030, 7224, 3612, 1032, 1},
{1, 2313, 9252, 21588, 32382, 32382, 21588, 9252, 2313, 1},
{1, 5130, 23085, 61560, 107730, 129276, 107730, 61560, 23085, 5130, 1}

Mathematica

Cp[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n - 2)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]];
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]

Crossrefs

Sequence in context: A168291 A154980 A166344 * A176152 A146958 A154653

Adjacent sequences: A146763 A146764 A146765 * A146767 A146768 A146769

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Nov 02 2008

Status

approved