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A065551
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Triangle of Faulhaber numbers (numerators) read by rows.
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3
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1, 0, 1, 0, -1, 1, 0, 1, -1, 1, 0, -3, 3, -1, 1, 0, 5, -5, 17, -2, 1, 0, -691, 691, -118, 41, -5, 1, 0, 35, -35, 359, -44, 14, -1, 1, 0, -3617, 3617, -1237, 1519, -293, 22, -7, 1, 0, 43867, -43867, 750167, -13166, 2829, -2258, 217, -4, 1, 0, -1222277, 1222277, -627073, 1540967, -198793, 689, -235, 46, -3, 1
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OFFSET
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0,12
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COMMENTS
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In the Gessel and Viennot reference f(n,k) = a(n,k)/A065553(n,k), n>=0, k>=0.
(n+1)*f(n,k) = A(n+1,n-k), with Knuth's A(m,k) =
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LINKS
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FORMULA
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sum(n>=0, k>=0, f(n, k)*t^k*x^(2*n+1)/(2*n+1)! ) is the expansion of (cosh(sqrt(1+4*t)*x/2)-cosh(x/2))/t/sinh(x/2).
a(n,k)=numerator(f(n,k)).
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EXAMPLE
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Triangle begins:
{1},
{0, 1},
{0, -1, 1},
{0, 1, -1, 1},
{0, -3, 3, -1, 1},
{0, 5, -5, 17, -2, 1}.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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