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A156691 General qp weighted combinations as : m=2;q=3: t(n,m)=If[m == 0, n!, Product[Product[1 - (i + 1)*(m + 1), {i, 0, k - 1}], {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])] 3
1, 1, 1, 1, -5, 1, 1, 40, 40, 1, 1, -440, 3520, -440, 1, 1, 6160, 542080, 542080, 6160, 1, 1, -104720, 129015040, -1419165440, 129015040, -104720, 1, 1, 2094400, 43865113600, 6755227494400, 6755227494400, 43865113600, 2094400, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, -3, 82, 2642, 1096482, -1161344798, 13598189404802, 633950903882665602,

301999235305843794118402, -782325471530406028574334585598,...},

LINKS

Table of n, a(n) for n=0..36.

FORMULA

m=2;q=3:

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

b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]

EXAMPLE

{1},

{1, 1},

{1, -5, 1},

{1, 40, 40, 1},

{1, -440, 3520, -440, 1},

{1, 6160, 542080, 542080, 6160, 1},

{1, -104720, 129015040, -1419165440, 129015040, -104720, 1},

{1, 2094400, 43865113600, 6755227494400, 6755227494400, 43865113600, 2094400, 1},

{1, -48171200, 20177952256000, -52825879006208000, 739562306086912000, -52825879006208000, 20177952256000, -48171200, 1},

{1, 1252451200, 12066415449088000, 631797512914247680000, 150367808073590947840000, 150367808073590947840000, 631797512914247680000, 12066415449088000, 1252451200, 1},

{1, -36321084800, 9098077248612352000, -10956632468958883266560000, 52153570552244284348825600000, -886610699388152833930035200000, 52153570552244284348825600000, -10956632468958883266560000, 9098077248612352000, -36321084800, 1}

MATHEMATICA

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

b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])];

Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}]

CROSSREFS

Sequence in context: A015116 A322220 A174790 * A246051 A111820 A174912

Adjacent sequences:  A156688 A156689 A156690 * A156692 A156693 A156694

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Feb 13 2009

STATUS

approved

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Last modified April 23 22:17 EDT 2019. Contains 322388 sequences. (Running on oeis4.)