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A174599 Triangle T(n,m)=A154646(n,m)-A154646(n,0)+1, 0<=k <=n. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified April 19 06:30 EDT 2019. Contains 322237 sequences. (Running on oeis4.)