A178640 Triangle T(n,k) with the coefficient [x^k] of the series (-1)^(n+1) * (x-1)^(n+1) * Sum_{j>=0} (5+8*j)^n*x^j in row n, column k.

1, 5, 3, 25, 94, 9, 125, 1697, 1223, 27, 625, 25436, 57926, 14236, 81, 3125, 352543, 1903218, 1513438, 159593, 243, 15625, 4717434, 52306583, 95276588, 34660263, 1766458, 729, 78125, 62123517, 1301287905, 4593751457, 3854897607, 738035607

Offset

0,2

Comments

Row sums are 1, 8, 128, 3072, 98304, 3932160, 188743680, 10569646080, 676457349120, 48704929136640, 3896394330931200, ....

Other pairs of consecutive Fibonacci numbers could be substituted for the two main parameters (5,8) in the definition. Using the pair (0,1) or (1,1) yields A008292. Using the pair (1,2) yields A060187.

Links

Table of n, a(n) for n=0..33.

Formula

T(n,0) = 5^n = A000351(n).

Example

1;
5, 3;
25, 94, 9;
125, 1697, 1223, 27;
625, 25436, 57926, 14236, 81;
3125, 352543, 1903218, 1513438, 159593, 243;
15625, 4717434, 52306583, 95276588, 34660263, 1766458, 729;
78125, 62123517, 1301287905, 4593751457, 3854897607, 738035607, 19469675, 2187;
390625, 812215096, 30495345372, 189174172168, 303412512454, 137293837704, 15054569308, 214299832, 6561;

Maple

A178640 := proc(n, k) (-1)^(n+1)*(x-1)^(n+1)*add( (5+8*j)^n*x^j, j=0..k) ; coeftayl(%, x=0, k) ; end proc: # R. J. Mathar, Apr 05 2011

Mathematica

Clear[m, m0, t, n, k]
m0 = {{1, 1}, {1, 0}}
m[l_] := MatrixPower[m0, l]
t[l_, k_] = If[l == 0, 1, m[l][[1, 1]]*k + m[l][[1, 2]]]
p[x_, n_, l_] := (-1)^(n + 1)*(-1 + x)^(n + 1)*Sum[t[l, k]^ n*x^k, {k, 0, Infinity}]
Table[Flatten[Table[CoefficientList[FullSimplify[ExpandAll[p[x, n, l]]], x], {n, 0, 10}]], {l, 0, 10}]

Crossrefs

Sequence in context: A032532 A111108 A038245 * A273153 A288812 A288898

Adjacent sequences: A178637 A178638 A178639 * A178641 A178642 A178643

Keyword

nonn,tabl

Author

Roger L. Bagula, May 31 2010

Status

approved