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A156699 General qp odd weighted factorial as antidiagonals: t(n,m)=If[m == 0, n!, Product[Product[1 - (2*i - 1)*( m + 1), {i, 0, k - 1}], {k, 1, n}]]. 0
1, 1, 1, 1, 3, 2, 1, 4, -9, 6, 1, 5, -32, -135, 24, 1, 6, -75, -2048, 18225, 120, 1, 7, -144, -12375, 1835008, 31984875, 720, 1, 8, -245, -48384, 38795625, 32883343360, -954268745625, 5040, 1, 9, -384, -145775, 390168576, 3283855678125 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 6, 2, -137, 16229, 33808092, -921346650220, -613200491632709703, 9136424641471148255125435, 4383291450735672536318454197723160,...}.

LINKS

Table of n, a(n) for n=0..41.

FORMULA

t(n,m)=If[m == 0, n!, Product[Product[1 - (2*i - 1)*( m + 1), {i, 0, k - 1}], {k, 1, n}]];

out_(n,m)=antidiagonal(t(n,m)).

EXAMPLE

{1},

{1, 1},

{1, 3, 2},

{1, 4, -9, 6},

{1, 5, -32, -135, 24},

{1, 6, -75, -2048, 18225, 120},

{1, 7, -144, -12375, 1835008, 31984875, 720},

{1, 8, -245, -48384, 38795625, 32883343360, -954268745625, 5040},

{1, 9, -384, -145775, 390168576, 3283855678125, -15321007338291200, -597882768540159375, 40320},

{1, 10, -567, -368640, 2515347625, 106974859493376, -9728668735621171875, -228427639649812348928000, 9364862009682718850390625, 362880},

{1, 11, -800, -821583, 12032409600, 1779495254044375, -1290517319364057759744, -1239342163515614410505859375, 129417671132618932648841052160000, 4253875018946507634823880419921875, 3628800}

MATHEMATICA

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

t[n_, m_] = If[m == 0, n!, Product[Product[1 - (2*i - 1)*(m + 1), {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[%]

CROSSREFS

Sequence in context: A159966 A119263 A028412 * A245183 A262347 A182236

Adjacent sequences:  A156696 A156697 A156698 * A156700 A156701 A156702

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Feb 13 2009

STATUS

approved

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Last modified September 22 12:52 EDT 2019. Contains 327307 sequences. (Running on oeis4.)