A146770 Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].

1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 7, 8, 7, 1, 1, 9, 13, 13, 9, 1, 1, 11, 21, 22, 21, 11, 1, 1, 13, 31, 39, 39, 31, 13, 1, 1, 15, 43, 66, 72, 66, 43, 15, 1, 1, 17, 57, 104, 131, 131, 104, 57, 17, 1, 1, 19, 73, 155, 225, 254, 225, 155, 73, 19, 1

Offset

0,5

Comments

Row sums are: {1, 2, 6, 12, 24, 46, 88, 168, 322, 620, 1200}.

Links

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

Example

Triangle begins:
{1},
{1, 1},
{1, 4, 1},
{1, 5, 5, 1},
{1, 7, 8, 7, 1},
{1, 9, 13, 13, 9, 1},
{1, 11, 21, 22, 21, 11, 1},
{1, 13, 31, 39, 39, 31, 13, 1},
{1, 15, 43, 66, 72, 66, 43, 15, 1},
{1, 17, 57, 104, 131, 131, 104, 57, 17, 1},
{1, 19, 73, 155, 225, 254, 225, 155, 73, 19, 1}

Mathematica

p[x_, n_] = If[ n == 0, 1, (x + 1)^n + Sum[Binomial[n-m, 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: A147289 A147566 A204621 * A143334 A156050 A136489

Adjacent sequences: A146767 A146768 A146769 * A146771 A146772 A146773

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Nov 02 2008

Status

approved