0,6

Row sums are:

{1, 2, 4, 75, 298192, 92582645347, 38552868375585686654,

408510417504770172006157933728171,

8252076335380285096546049596012569615906231164892,

304054204703125404182090464876531072208919935961849569542226739902869,

204395544426610196275031273695780445058541490048388479325449151028537542028112

71948347587714,...}.

This result comes from truncated versions of:

1/(1-(-(x + x^2 + x^3 + x^4 + x^5 - x^7)))=Sum[(-(x + x^2 + x^3 + x^4 + x^5 - x^7))^k, {k, 0, Infinity}].

as polynomials.

The q-combinations that result appear to be 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^7 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 + (1 + m)^2 + (1 + m)^3 + (1 + m)^4 + (1 + m)^5 - (1 + m)^7))^i, {i, 0, k - 1}], {k, 1, n}]];

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

{1},

{1, 1},

{1, 1, 2},

{1, 1, 67, 6},

{1, 1, 1825, 296341, 24},

{1, 1, 15021, 6075061825, 86507568379, 120},

{1, 1, 74221, 3388969238841, 36886153511769270625, 1666711474847102245, 720},

{1, 1, 270607, 408859932813241, 11484347898092358710495061, 408508286631392559053881969770625, 2119389029714451057320373595, 5040},

{1, 1, 803937, 19815976339460701, 167164192380442041912182352661, 584541010846308862037287070883402354183681, 8252075750661403361683171657786324640611743390625, 177870888386851708558712234003610932965, 40320},

{1, 1, 2059705, 519595654635081921, 392671467204171617161382535724159, 5072626731525894581861015650056935972418391092481, 446882723322765678880018961600203886522524539878111886575752701, 304053757820402080426096765933253718182714609813607042661687255890625, 985242192192789858847786320769473576039197343938395, 362880},

{1, 1, 4716541, 8738056709406200305, 269979308493767420077156125384212769, 2105623102864030124492652895415473068862186529726486245, 11424665874203147275989825110391859442320460006786242223207380136473520701, 513147333339511828959372769242262419088114593191930513131453903655862180030202 5586970121, 204344229693276244977888674074979369239979437292953072206231164087678778691030 99696800390625, 360184537679569875916355731839707391944353834991023090724961461605, 3628800}

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

t[n_, m_] = If[m == 0, n!, Product[Sum[(-( 1 + m + (1 + m)^2 + (1 + m)^3 + (1 + m)^4 + (1 + m)^5 - (1 + m)^7))^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: A093076 A132454 A058293 this_sequence A159767 A164810 A089538

Adjacent sequences: A156885 A156886 A156887 this_sequence A156889 A156890 A156891

nonn,tabl,uned

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