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A225356 Apply the triangle-to-triangle transformation described in the Comments in A159041 to the triangle in A060187. 3
1, 1, 1, 1, -22, 1, 1, -75, -75, 1, 1, -236, 1446, -236, 1, 1, -721, 9822, 9822, -721, 1, 1, -2178, 58479, -201244, 58479, -2178, 1, 1, -6551, 325061, -2160227, -2160227, 325061, -6551, 1, 1, -19672, 1736668, -19971304 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, -20, -148, 976, 18204, -88640, -3683432, 12933376, 1154867500,...}.

LINKS

Table of n, a(n) for n=0..39.

FORMULA

A triangle of polynomial coefficients: p(x,n)=Sum[x^i*If[i == Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= (less than or equal to) Floor[n/2], (-1)^i*A060187[n+1, i+1], -(-1)^(n - i)*A060187[n+1, i+1]]], {i, 0, n}]/(1 - x).

EXAMPLE

The triangle begins:

{1},

{1, 1},

{1, -22, 1},

{1, -75, -75, 1},

{1, -236, 1446, -236, 1},

{1, -721, 9822, 9822, -721, 1},

{1, -2178, 58479, -201244, 58479, -2178, 1},

{1, -6551, 325061, -2160227, -2160227, 325061, -6551, 1},

{1, -19672, 1736668, -19971304, 49441990, -19971304, 1736668, -19672,1},...

MATHEMATICA

q[x_, n_] = (-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(2*m + 1)^n*x^m, {m, 0, Infinity}];

t[n_, m_] := Table[CoefficientList[FullSimplify[ExpandAll[q[x, k]]], x], {k, 0, 10}][[n + 1, m + 1]]; p[x_, n_] = Sum[x^i*If[i == Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= Floor[n/2], (-1)^i*t[n, i], -(-1)^(n - i)*t[n, i]]], {i, 0, n}]/(1 - x); Flatten[Table[

  CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 1, 10}]]

CROSSREFS

Cf A007318, A060187, A159041.

Sequence in context: A040486 A040485 A040484 * A291072 A174599 A291074

Adjacent sequences:  A225353 A225354 A225355 * A225357 A225358 A225359

KEYWORD

sign,tabl

AUTHOR

Roger L. Bagula, May 07 2013

EXTENSIONS

Edited by N. J. A. Sloane, May 11 2013

STATUS

approved

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Last modified May 14 14:36 EDT 2021. Contains 343884 sequences. (Running on oeis4.)