A155725 Symmetrical product form polynomial as triangle sequence coefficients: q(x,n)=Product[x + 2*n - i + 1, {i, 0, n - 1}]; p(x,n)=q(x,n)+x^2+x^n*q(1/x,m);t(n,m)=coefficients(p(x,n).

2, 4, 4, 21, 18, 21, 211, 125, 125, 211, 3025, 1680, 670, 1680, 3025, 55441, 31639, 7960, 7960, 31639, 55441, 1235521, 725655, 178199, 45570, 178199, 725655, 1235521, 32432401, 19471584, 4988326, 765289, 765289, 4988326, 19471584

Offset

0,1

Comments

Row sums are:

{2, 8, 60, 672, 10080, 190080, 4324320, 115315200, 3528645120, 121898649600,

4693098009600,...}.

Links

Table of n, a(n) for n=0..34.

Formula

q(x,n)=Product[x + 2*n - i + 1, {i, 0, n - 1}];

p(x,n)=q(x,n)+x^2+x^n*q(1/x,m);

t(n,m)=coefficients(p(x,n).

Example

{2},
{4, 4},
{21, 18, 21},
{211, 125, 125, 211},
{3025, 1680, 670, 1680, 3025},
{55441, 31639, 7960, 7960, 31639, 55441},
{1235521, 725655, 178199, 45570, 178199, 725655, 1235521},
{32432401, 19471584, 4988326, 765289, 765289, 4988326, 19471584, 32432401},
{980179201, 598482108, 159173510, 24219972, 4535538, 24219972, 159173510, 598482108, 980179201}, {33522128641, 20742534711, 5681716170, 904550030, 98395248, 98395248, 904550030, 5681716170, 20742534711, 33522128641},
{1279935820801, 800575997925, 224518871346, 37179349350, 4041096653, 595737450, 4041096653, 37179349350, 224518871346, 800575997925, 1279935820801}

Mathematica

Clear[p, a, b, c, d, n, q, q2, x];
q[x_, n_] = Product[x + 2*n - i + 1, {i, 0, n - 1}];
p[x_, n_] = q[x, n] + x^n*q[1/x, n];
Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A241211 A155720 A230694 * A103973 A322635 A129826

Adjacent sequences: A155722 A155723 A155724 * A155726 A155727 A155728

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Jan 25 2009

Status

approved