A146767 Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].

1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 20, 30, 20, 1, 1, 45, 90, 90, 45, 1, 1, 102, 255, 340, 255, 102, 1, 1, 231, 693, 1155, 1155, 693, 231, 1, 1, 520, 1820, 3640, 4550, 3640, 1820, 520, 1, 1, 1161, 4644, 10836, 16254, 16254, 10836, 4644, 1161, 1, 1, 2570, 11565, 30840, 53970

Offset

0,5

Comments

Row sums are: {1, 2, 6, 20, 72, 272, 1056, 4160, 16512, 65792, 262656}.

Links

Table of n, a(n) for n=0..59.

Example

Triangle begins:
{1},
{1, 1},
{1, 4, 1},
{1, 9, 9, 1},
{1, 20, 30, 20, 1},
{1, 45, 90, 90, 45, 1},
{1, 102, 255, 340, 255, 102, 1},
{1, 231, 693, 1155, 1155, 693, 231, 1},
{1, 520, 1820, 3640, 4550, 3640, 1820, 520, 1},
{1, 1161, 4644, 10836, 16254, 16254, 10836, 4644, 1161, 1},
{1, 2570, 11565, 30840, 53970, 64764, 53970, 30840, 11565, 2570, 1}

Mathematica

p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n - 3)*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: A157192 A154982 A347972 * A146955 A155451 A220681

Adjacent sequences: A146764 A146765 A146766 * A146768 A146769 A146770

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Nov 02 2008

Status

approved