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A154854 Symmetrical triangular sequence: p(x,n) =((-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(4*m + 3)^ n*x^m, {m, 0, Infinity}] - (-1)^(n + 1)*(x - 1)^(n + 1)* Sum[(4*m + 1)^n*x^m, {m, 0, Infinity}])/2. 0
1, -1, 4, 0, -4, 13, 57, -57, -13, 40, 688, 0, -688, -40, 121, 6115, 11770, -11770, -6115, -121, 364, 48464, 270620, 0, -270620, -48464, -364, 1093, 363965, 4401033, 5613265, -5613265, -4401033, -363965, -1093, 3280, 2657568, 61590368 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums are zero.

LINKS

Table of n, a(n) for n=0..37.

FORMULA

p(x,n) = ((-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(4*m + 3)^ n*x^m, {m, 0, Infinity}]

- (-1)^(n + 1)*(x - 1)^(n + 1)* Sum[(4*m + 1)^n*x^m, {m, 0, Infinity}])/2;

t(n,m)=coefficients(p(x,n))

EXAMPLE

{},

{1, -1},

{4, 0, -4},

{13, 57, -57, -13},

{40, 688, 0, -688, -40},

{121, 6115, 11770, -11770, -6115, -121},

{364, 48464, 270620, 0, -270620, -48464, -364},

{1093, 363965, 4401033, 5613265, -5613265, -4401033, -363965, -1093},

{3280, 2657568, 61590368, 199134880, 0, -199134880, -61590368, -2657568, -3280},

{9841, 19101831, 793704036, 4929623916, 4890510366, -4890510366, -4929623916, -793704036, -19101831, -9841},

{29524, 136030048, 9727040988, 103412071488, 239084539848, 0, -239084539848, -103412071488, -9727040988, -136030048, -29524}

MATHEMATICA

Clear[p]; p[x_, n_] = ((-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(4*m + 3)^ n*x^m, {m, 0, Infinity}]

- (-1)^(n + 1)*(x - 1)^(n + 1)* Sum[(4*m + 1)^n*x^m, {m, 0, Infinity}])/2;

Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];

Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A209134 A281297 A058536 * A151672 A058493 A112149

Adjacent sequences:  A154851 A154852 A154853 * A154855 A154856 A154857

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Jan 16 2009

STATUS

approved

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Last modified October 23 05:49 EDT 2018. Contains 316519 sequences. (Running on oeis4.)