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A243034
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Expansion of A(x) = x*F'(x)/(F(x) - F(x)^2), where F(x) = (-1 - sqrt(1-8*x) + sqrt(2 + 2*sqrt(1-8*x) + 8*x))/4.
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1
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1, 2, 10, 62, 422, 2992, 21736, 160442, 1197798, 9018656, 68355820, 520851212, 3986036204, 30615867128, 235879185188, 1822138940482, 14108173076358, 109454660444336, 850687921793836, 6622072711690452
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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) = 1 + n*Sum_{m=0..n} ( Sum_{k=1..(n-m)} (binomial(k, n-m-k) * binomial(n+2*k-1, n+k-1))/(n+k))).
G.f.: A(x) = x*F'(x)/(F(x)-F(x)^2), where F(x)/x is g.f. of A186997.
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MATHEMATICA
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Table[1+n*Sum[Sum[Binomial[k, n-m-k]*Binomial[n+2*k-1, n+k-1]/(n+k), {k, 1, n-m}], {m, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, May 31 2014 after Vladimir Kruchinin *)
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PROG
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(Maxima) a(n):=1+n*sum(sum((binomial(k, n-m-k)*binomial(n+2*k-1, n+k-1))/(n+k), k, 1, n-m), m, 0, n);
(PARI) for(n=0, 25, print1(1 + n*sum(m=0, n, sum(k=1, n-m, (binomial(k, n-m-k)*binomial(n+2*k-1, n+k-1))/(n+k))), ", ")) \\ G. C. Greubel, Jun 01 2017
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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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