A146772 Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n-1)*Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].

1, 1, 1, 1, 6, 1, 1, 11, 11, 1, 1, 28, 22, 28, 1, 1, 69, 58, 58, 69, 1, 1, 166, 207, 84, 207, 166, 1, 1, 391, 661, 291, 291, 661, 391, 1, 1, 904, 1948, 1336, 326, 1336, 1948, 904, 1, 1, 2057, 5412, 5204, 1406, 1406, 5204, 5412, 2057, 1, 1, 4618, 14381, 18040, 7890

Offset

0,5

Comments

Row sums are: {1, 2, 8, 24, 80, 256, 832, 2688, 8704, 28160, 91136}.

Links

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

Example

Triangle begins:
{1},
{1, 1},
{1, 6, 1},
{1, 11, 11, 1},
{1, 28, 22, 28, 1},
{1, 69, 58, 58, 69, 1},
{1, 166, 207, 84, 207, 166, 1},
{1, 391, 661, 291, 291, 661, 391, 1},
{1, 904, 1948, 1336, 326, 1336, 1948, 904, 1},
{1, 2057, 5412, 5204, 1406, 1406, 5204, 5412, 2057, 1},
{1, 4618, 14381, 18040, 7890, 1276, 7890, 18040, 14381, 4618, 1}

Mathematica

p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n-1)*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: A131063 A081579 A295707 * A202868 A202877 A174124

Adjacent sequences: A146769 A146770 A146771 * A146773 A146774 A146775

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Nov 02 2008

Status

approved