A174599 Triangle T(n,m)=A154646(n,m)-A154646(n,0)+1, 0<=k <=n.

1, 1, 1, 1, 22, 1, 1, 145, 145, 1, 1, 780, 2246, 780, 1, 1, 3919, 25144, 25144, 3919, 1, 1, 19202, 243047, 524812, 243047, 19202, 1, 1, 93349, 2168107, 8760511, 8760511, 2168107, 93349, 1, 1, 453592, 18445564, 127880680, 235517062, 127880680

Offset

0,5

Comments

The first and last element of each row of A154646 are reduced to 1 by subtracting a constant from each row.

Row sums are 1, 2, 24, 292, 3808, 58128, 1049312, 22043936, 529076736, 14285128960,

428554011136,...

Links

Table of n, a(n) for n=0..41.

Example

1;
1, 1;
1, 22, 1;
1, 145, 145, 1;
1, 780, 2246, 780, 1;
1, 3919, 25144, 25144, 3919, 1;
1, 19202, 243047, 524812, 243047, 19202, 1;
1, 93349, 2168107, 8760511, 8760511, 2168107, 93349, 1;
, 453592, 18445564, 127880680, 235517062, 127880680, 18445564, 453592, 1;
1, 2209627, 152441218, 1711859374, 5276054260, 5276054260, 1711859374, 152441218, 2209627, 1;

Mathematica

Clear[p];
p[x_, n_] = (-1)^(n + 1)*(x - 1)^( n + 1)*Sum[(3*m + 2)^n*x^m, {m, 0, Infinity}] + (-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(3*m + 1)^n*x^m, {m, 0, Infinity}];
Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];
a0 = Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
Table[Table[a0[[n]][[m]] - a0[[n]][[1]] + 1, {m, 1, Length[a0[[n]]]}], {n, 1, Length[a0]}];
Flatten[%]

Crossrefs

Sequence in context: A040484 A225356 A291072 * A291074 A225076 A022185

Adjacent sequences: A174596 A174597 A174598 * A174600 A174601 A174602

Keyword

nonn,tabl

Author

Roger L. Bagula, Mar 23 2010

Status

approved