A174678 Sequence A154647 adjusted to leading ones:t(n,m)=A154647(n,m)-A154647(n,0)+1

1, 1, 1, 1, 18, 1, 1, 165, 165, 1, 1, 1268, 3406, 1268, 1, 1, 9113, 51963, 51963, 9113, 1, 1, 63718, 692343, 1434448, 692343, 63718, 1, 1, 440989, 8557937, 32284381, 32284381, 8557937, 440989, 1, 1, 3044904, 101118220, 641504248, 1151047254

Offset

0,5

Comments

Row sums are:

{1, 2, 20, 332, 5944, 122154, 2946572, 82566616, 2642382000, 95126716310,

3805072264036,...}

Links

Table of n, a(n) for n=0..40.

Formula

t(n,m)=A154647(n,m)-A154647(n,0)+1

Example

{1},
{1, 1},
{1, 18, 1},
{1, 165, 165, 1},
{1, 1268, 3406, 1268, 1},
{1, 9113, 51963, 51963, 9113, 1},
{1, 63718, 692343, 1434448, 692343, 63718, 1},
{1, 440989, 8557937, 32284381, 32284381, 8557937, 440989, 1},
{1, 3044904, 101118220, 641504248, 1151047254, 641504248, 101118220, 3044904, 1},
{1, 21045105, 1161583479, 11747799063, 34632930507, 34632930507, 11747799063, 1161583479, 21045105, 1},
{1, 145766138, 13106374045, 203453014612, 928796814694, 1514068325056, 928796814694, 203453014612, 13106374045, 145766138, 1}

Mathematica

p[x_, n_] = (1 - x)^(n + 1)*(Sum[(4*k + 1)^n*x^k, {k, 0, Infinity}] + Sum[(4*k + 3)^n*x^k, {k, 0, Infinity}])/2;
a = Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
t[n_, m_] := a[[n + 1]][[m + 1]];
Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

A154647

Sequence in context: A155497 A202677 A179838 * A167884 A022181 A015144

Adjacent sequences: A174675 A174676 A174677 * A174679 A174680 A174681

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 26 2010

Status

approved