A141684 - OEIS

A141684

Triangle read by rows formed from Euler polynomials: p(x,n) = if(n mod 2 = 1, 2^(1 + ((n - 1)/2))*EulerE(n, x), EulerE(n, x)); t(n,m) = Coefficients(p(x,n)).

1, -1, 2, 0, -1, 1, 1, 0, -6, 4, 0, 1, 0, -2, 1, -4, 0, 20, 0, -20, 8, 0, -3, 0, 5, 0, -3, 1, 34, 0, -168, 0, 140, 0, -56, 16, 0, 17, 0, -28, 0, 14, 0, -4, 1, -496, 0, 2448, 0, -2016, 0, 672, 0, -144, 32, 0, -155, 0, 255, 0, -126, 0, 30, 0, -5, 1

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OFFSET

1,3

COMMENTS

Row sums are {1, 1, 0, -1, 0, 4, 0, -34, 0, 496, 0, ...}.

LINKS

G. C. Greubel, Rows n=1..100 of triangle, flattened

EXAMPLE

{ 1},

{ -1, 2},

{ 0, -1, 1},

{ 1, 0, -6, 4},

{ 0, 1, 0, -2, 1},

{ -4, 0, 20, 0, -20, 8},

{ 0, -3, 0, 5, 0, -3, 1},

{ 34, 0, -168, 0, 140, 0, -56, 16},

{ 0, 17, 0, -28, 0, 14, 0, -4, 1},

{-496, 0, 2448, 0, -2016, 0, 672, 0, -144, 32},

{ 0, -155, 0, 255, 0, -126, 0, 30, 0, -5, 1}

MATHEMATICA

T[x_, n_] := If[Mod[n, 2] == 1, 2^(1 + ((n - 1)/2))*EulerE[n, x], EulerE[n, x]]; Table[Expand[T[x, n]], {n, 0, 10}]; Table[CoefficientList[T[x, n], x], {n, 0, 10}]; Flatten[%]

CROSSREFS

Cf. A060083, A004172, etc.

Sequence in context: A307039 A243046 A058940 * A152492 A075446 A184159

Adjacent sequences: A141681 A141682 A141683 * A141685 A141686 A141687

KEYWORD

tabl,sign

AUTHOR

Roger L. Bagula and Gary W. Adamson, Sep 08 2008

EXTENSIONS

Edited by N. J. A. Sloane, Jan 06 2009

STATUS

approved