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A071723
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Expansion of (1+x^2*C^2)*C^4, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
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0
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1, 4, 15, 54, 192, 682, 2431, 8710, 31382, 113696, 414086, 1515516, 5571750, 20569590, 76228095, 283481670, 1057628550, 3957577800, 14849601090, 55859886420, 210622646520, 795898303668, 3013646759910, 11432740177564, 43448822603452, 165396657221152
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (Sum_{k=0..n} (k+1)*(k^2+k+1)*binomial(2*n-k,n))/(n+1). - Vladimir Kruchinin, Sep 28 2011
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PROG
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(Maxima) a(n):=sum((k+1)*(k^2+k+1)*binomial(2*n-k, n), k, 0, n)/(n+1); /* Vladimir Kruchinin, Sep 28 2011 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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