0,6

Row sums are:

{1, 2, 4, 29, 9282, 145754581, 5084224532623360, 149349458957160053190989915,

1820798766324444943660692219703051336476,

9195862075610185754335952791821128886343190896895732961,

22327760468844996026083909497741530196426984991348912790632217727403786174,...}.

This result comes from truncated versions of:

-1/(-1 + x^2 - x^4 - x^5 + x^6)=Sum[((x^2 - x^4 - x^5 + x^6))^k, {k, 0, Infinity}].

as polynomials.

The q-combinations that result are higher odd q-combinations of the Gaussian type.

They are at the very least very high integer q-type combinations.

There exists the possibility that the q-combinations being Gaussian

is connected to the minimal Pisot condition?

If that conjecture is true, then this is the next (x^6 level) minimal Pisot

as has been conjectured but not proved.

A. K. Kwasniewski, This is the definition which is the right answer to the leitmotiv questions, arXiv:0902.2827v1 [v1] Tue, 17 Feb 2009 04:02:30 GMT; http://ii.uwb.edu.pl/akk/sem/subjects/sub2.htm

t(n,m)=If[m == 0, n!, Product[Sum[((1 + m)^2 - (1 + m)^4 - (1 + m)^5 + (1 + m)^6)^i, {i, 0, k - 1}], {k, 1, n}]];

out_(n,m)=anti=diagonal(t(n,m)).

{1},

{1, 1},

{1, 1, 2},

{1, 1, 21, 6},

{1, 1, 415, 8841, 24},

{1, 1, 2833, 71301565, 74450061, 120},

{1, 1, 11901, 22729320481, 5071662849566575, 12538953723681, 720}, {

1, 1, 37621, 1685442243801, 516439650916945061425, 149348900281032409928364325, 42236475040875277701, 5040},

{1, 1, 98491, 53245077332041, 2840476861656042162085701, 33231194674669854682930125289391425, 1820765535126922028697037902373869508375, 2845404632109677916652880121, 40320},

{1, 1, 225345, 955399987806181, 2834962902229523240727202861, 56965983315187513139032833264900659537601, 6055717113602108237045789460300557575690267444467025, 9189806358496526676281783465741023760324596394342072125, 3833808346271702633379160693734058941, 362880},

{1, 1, 465913, 11443051477794945, 912779868958464202149979739971, 5678506005569432364896166433584652557296050081, 13595240734604594344784540439658093064836176712840374493599501, 3125204587345356383944286104959125340957059369108988879466334816219555425, 19202555881486044401405018689448068346972521622874916944579112299076849375, 103311045962488312628624135397813632478856102161, 3628800}

Clear[t, n, m, i, k, a, b];

t[n_, m_] = If[m == 0, n!, Product[Sum[((1 + m)^2 - (1 + m)^4 - (1 + m)^5 + (1 + m)^6)^i, {i, 0, k - 1}], {k, 1, n}]];

a = Table[Table[t[n, m], {n, 0, 10}], {m, 0, 10}];

b = Table[Table[a[[m, n - m + 1]], {m, n, 1, -1}], {n, 1, Length[a]}];

Flatten[%]

Sequence in context: A090163 A124001 A157453 this_sequence A156725 A141904 A147802

Adjacent sequences: A156886 A156887 A156888 this_sequence A156890 A156891 A156892

nonn,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 17 2009