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A172429 Alternating q-form-Pascal triangle sequence:f(n,q)=If[Mod[1 - q^n, 2] == 0, , If[Mod[n, 2] == 0, (1 - q^n), n! ], If[Mod[n, 2] == 1, n!, (1 - q^n)]];q=4;c(n,q)=Product[f(i, q), {i, 1, n}];t(n,m,q)=c(n, q)/(c(m, q)*c(n - m, q)) 0
1, 1, 1, 1, -15, 1, 1, 6, 6, 1, 1, -255, 102, -255, 1, 1, 120, 2040, 2040, 120, 1, 1, -4095, 32760, -1392300, 32760, -4095, 1, 1, 5040, 1375920, 27518400, 27518400, 1375920, 5040, 1, 1, -65535, 22019760, -15028486200, 7072228800, -15028486200, 22019760 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, -13, 14, -406, 4322, -1334968, 57798722, -22940835148, 45439521523202,

-176478793961380348,...}

LINKS

Table of n, a(n) for n=0..42.

FORMULA

f(n,q)=If[Mod[1 - q^n, 2] == 0, If[Mod[n, 2] == 0, (1 - q^n), n! ], If[Mod[n, 2] == 1, n!, (1 - q^n)]];

q=4

;c(n,q)=Product[f(i, q), {i, 1, n}];

t(n,m,q)=c(n, q)/(c(m, q)*c(n - m, q))

EXAMPLE

{1},

{1, 1},

{1, -15, 1},

{1, 6, 6, 1},

{1, -255, 102, -255, 1},

{1, 120, 2040, 2040, 120, 1},

{1, -4095, 32760, -1392300, 32760, -4095, 1},

{1, 5040, 1375920, 27518400, 27518400, 1375920, 5040, 1},

{1, -65535, 22019760, -15028486200, 7072228800, -15028486200, 22019760, -65535, 1},

{1, 362880, 1585422720, 1331755084800, 21386419891200, 21386419891200, 1331755084800, 1585422720, 362880, 1},

{1, -1048575, 25367126400, -277072438104000, 5476255247232000, -186877210311792000, 5476255247232000, -277072438104000, 25367126400, -1048575, 1}

MATHEMATICA

Clear[t, n, m, c, q];

f[n_, q_] = If[Mod[1 - q^n, 2] == 0, If[Mod[n, 2] == 0, (1 - q^n), n! ], If[Mod[n, 2] == 1, n!, (1 - q^n)]];

c[n_, q_] = Product[f[i, q], {i, 1, n}];

t[n_, m_, q_] = c[n, q]/(c[m, q]*c[n - m, q]);

Table[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}], {q, 2, 12}];

Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]

CROSSREFS

Sequence in context: A281571 A040227 A040226 * A040225 A070644 A174389

Adjacent sequences:  A172426 A172427 A172428 * A172430 A172431 A172432

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Feb 02 2010

STATUS

approved

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Last modified March 19 17:38 EDT 2019. Contains 321330 sequences. (Running on oeis4.)