OFFSET
0,2
COMMENTS
Row sums are 1, 8, 128, 3072, 98304, 3932160, 188743680, 10569646080, 676457349120, 48704929136640, 3896394330931200, ....
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
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, May 31 2010
STATUS
approved