A155720 Triangle read by rows: let f(n,m)=Product[k + m + 1, {k, 0, n}]; t0(n,m)=f(n, m)/(f(n - m, m)); then t(n,m)=t0(n,m)+t0(n,n-m).

2, 4, 4, 21, 8, 21, 211, 35, 35, 211, 3025, 342, 84, 342, 3025, 55441, 5047, 560, 560, 5047, 55441, 1235521, 95048, 7992, 1440, 7992, 95048, 1235521, 32432401, 2162169, 154530, 12870, 12870, 154530, 2162169, 32432401, 980179201, 57657610, 3603710

Offset

0,1

Comments

Row sums are: {2, 8, 50, 492, 6818, 122096, 2678562, 69523940, 2083398482, 70781242248, 2688204949586,...}.

The sequence has an interesting inverted center structure and is based on a generalized permutation product form.

Links

Table of n, a(n) for n=0..38.

Formula

f(n,m)=Product[k + m + 1, {k, 0, n}];

t0(n,m)=f(n, m)/(f(n - m, m));

t(n,m)=t0(n,m)+t0(n,n-m).

Example

{2},
{4, 4},
{21, 8, 21},
{211, 35, 35, 211},
{3025, 342, 84, 342, 3025},
{55441, 5047, 560, 560, 5047, 55441},
{1235521, 95048, 7992, 1440, 7992, 95048, 1235521},
{32432401, 2162169, 154530, 12870, 12870, 154530, 2162169, 32432401},
{980179201, 57657610, 3603710, 241560, 34320, 241560, 3603710, 57657610, 980179201},
{33522128641, 1764322571, 98018052, 5767476, 384384, 384384, 5767476, 98018052, 1764322571, 33522128641},
{1279935820801, 60949324812, 3047466396, 160395144, 8943480, 1048320, 8943480, 160395144, 3047466396, 60949324812, 1279935820801}

Mathematica

Clear[f, t, n, m, k];
f[n_, m_] := Product[k + m + 1, {k, 0, n}];
t[n_, m_] := f[n, m]/(f[n - m, m]);
Table[Table[t[n, m] + t[n, n - m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A013140 A326773 A241211 * A230694 A155725 A103973

Adjacent sequences: A155717 A155718 A155719 * A155721 A155722 A155723

Keyword

nonn,tabl

Author

Roger L. Bagula, Jan 25 2009

Extensions

Edited by N. J. A. Sloane, Jan 31 2009

Status

approved