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A176332
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Row sums of triangle A176331.
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3
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1, 2, 5, 16, 56, 202, 741, 2752, 10318, 38972, 148070, 565280, 2166646, 8332378, 32136205, 124249856, 481433286, 1868972828, 7267804550, 28304698336, 110383060776, 431000853028, 1684754608210, 6592277745536, 25818887839956
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OFFSET
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0,2
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COMMENTS
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Hankel transform is A176333.
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LINKS
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Table of n, a(n) for n=0..24.
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FORMULA
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a(n)=sum{k=0..n, sum{j=0..n, C(j,n-k)*C(j,k)*(-1)^(n-j)}}.
Logarithm g.f. atan(x*C(x))=sum(n>0, a(n)/n*x^n), C(x)=(1-sqrt(1-4*x))/(2*x) (A000108) [From Vladimir Kruchinin, Aug 10 2010]
Conjecture: 6*n*a(n) +2*(-17*n+10)*a(n-1) +(47*n-60)*a(n-2) +10*(-3*n+5)*a(n-3) +4*(2*n-5)*a(n-4)=0. - R. J. Mathar, Nov 24 2012
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MATHEMATICA
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f[n_] := (-1)^n*Sum[ Binomial[n + k, k] Cos[Pi (n + k)/2], {k, 0, n}]; Array[f, 24, 0] (* Robert G. Wilson v, Apr 02 2012 *)
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CROSSREFS
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Sequence in context: A137732 A057973 A102461 * A191241 A052708 A149973
Adjacent sequences: A176329 A176330 A176331 * A176333 A176334 A176335
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Apr 15 2010
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STATUS
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approved
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