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A192063
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E.g.f. 1-sqrt(cos(2*x)) (even part).
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0
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0, 2, 4, 152, 8944, 933152, 151557184, 35402298752, 11250504212224, 4668840721981952, 2451963626804184064, 1589715293557268682752, 1247113599659216858312704, 1164315843409068590677041152, 127574292191869924893941171814
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..14.
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FORMULA
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a(n) = sum((k=1..2*n, binomial(2*k-2,k-1)*2^(2*n-2*k+2)*sum(j=1..k, ((sum(i=0..(j-1)/2, (j-2*i)^(2*n)*binomial(j,i)))*binomial(k,j)*(-1)^(n-j))/2^j))/k).
a(n) = 2*sum(k=1..2*n, C(k-1)*sum(i=0..k-1, (i-k)^(2*n)*binomial(2*k,i)*(-1)^(n+k-i))*2^(2*n-3*k+1)), where C(k) = A000108(k). - Vladimir Kruchinin, Oct 05 2012
G.f.: 1 - 1/U(0) where U(k)= 1 - (2*k-1)*(2*k+2)*x/U(k+1);(continued fraction, due Stiltjes T.J, 1-step). - Sergei N. Gladkovskii, Nov 09 2012
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PROG
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(Maxima)
a(n):=sum((binomial(2*k-2, k-1)*2^(2*n-2*k+2)*sum(((sum((j-2*i)^(2*n) *binomial(j, i), i, 0, (j-1)/2))*binomial(k, j)*(-1)^(n-j))/2^j, j, 1, k))/k, k, 1, 2*n);
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CROSSREFS
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Sequence in context: A018517 A018539 A018544 * A018558 A132528 A018573
Adjacent sequences: A192060 A192061 A192062 * A192064 A192065 A192066
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KEYWORD
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nonn
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AUTHOR
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Vladimir Kruchinin, Jun 22 2011
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STATUS
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approved
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