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A230011
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Numerators of sum of rows of the inverse of the triangle of Euler polynomial coefficients P(0,x)=1, 2P(n,x)=(1+x)*[(1+x)^(n-1)+x^(n-1)].
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1
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1, 0, 1, -1, 1, -1, 3, -3, -11, 11, 113, -113, -1269, 1269, 20575, -20575, -888419, 888419, 24729909, -24729909, -862992415, 862992415, 36913939753, -36913939753, -1899853421901, 1899853421901, 115841483491307, -115841483491307
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OFFSET
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0,7
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COMMENTS
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Denominators are 1, 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 32, 32, ..., a sequence which matches A053644, except the first term.
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LINKS
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EXAMPLE
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1, 0, 1/2, -1/2, 1/4, -1/4, 3/4, -3/4, -11/8, 11/8, 113/8, -113/8, ...
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MATHEMATICA
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max = 30; p[0, _] = 1; p[n_, x_] := (1+x)*((1+x)^(n-1)+x^(n-1))/2; t = Total /@ Inverse @ Table[Coefficient[p[n, x], x, k], {n, 0, max+2}, {k, 0, max+2}]; a[n_] := t[[n+1]] // Numerator; Table[a[n], {n, 0, max}]
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CROSSREFS
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KEYWORD
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sign,frac,easy
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AUTHOR
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STATUS
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approved
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