A146774 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, 18, 1, 1, 35, 35, 1, 1, 100, 70, 100, 1, 1, 261, 202, 202, 261, 1, 1, 646, 783, 276, 783, 646, 1, 1, 1543, 2581, 1059, 1059, 2581, 1543, 1, 1, 3592, 7708, 5176, 1094, 5176, 7708, 3592, 1, 1, 8201, 21540, 20564, 5246, 5246, 20564, 21540, 8201, 1, 1

Offset

0,5

Comments

Row sums are: {1, 2, 20, 72, 272, 928, 3136, 10368, 34048, 111104, 361472}.

Links

Table of n, a(n) for n=0..55.

Example

Triangle begins:
{1},
{1, 1},
{1, 18, 1},
{1, 35, 35, 1},
{1, 100, 70, 100, 1},
{1, 261, 202, 202, 261, 1},
{1, 646, 783, 276, 783, 646, 1},
{1, 1543, 2581, 1059, 1059, 2581, 1543, 1},
{1, 3592, 7708, 5176, 1094, 5176, 7708, 3592, 1},
{1, 8201, 21540, 20564, 5246, 5246, 20564, 21540, 8201, 1},
{1, 18442, 57389, 71800, 30930, 4348, 30930, 71800, 57389, 18442, 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: A040325 A040324 A168623 * A174451 A144405 A202671

Adjacent sequences: A146771 A146772 A146773 * A146775 A146776 A146777

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Nov 02 2008

Status

approved