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A184889
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a(n) = (5^n/n!^2) * Product_{k=0..n-1} (10k+2)*(10k+3).
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2
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1, 30, 5850, 1644500, 542685000, 196017822000, 75031266310000, 29905319000700000, 12279871614662437500, 5159062111690898125000, 2207046771381366217875000, 958150139674902210123750000
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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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Self-convolution yields Sum_{k=0..n} a(n-k)*a(k) = A184890(n) where A184890(n) = C(2n,n) * (5^n/n!^2)*Product_{k=0..n-1} (5k+2)*(5k+3).
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EXAMPLE
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G.f.: A(x) = 1 + 30*x + 5850*x^2 + 1644500*x^3 +...
A(x)^2 = 1 + 60*x + 12600*x^2 + 3640000*x^3 +...+ A184890(n)*x^n +...
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MATHEMATICA
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FullSimplify[Table[500^n * Gamma[n+1/5] * Gamma[n+3/10] / (Gamma[n+1]^2 * Gamma[1/5] * Gamma[3/10]), {n, 0, 15}]] (* Vaclav Kotesovec, Jul 03 2014 *)
Join[{1}, With[{nn=15}, Table[5^n/(n!)^2, {n, nn}] Rest[FoldList[Times, 1, Table[ (10k+2)(10k+3), {k, 0, nn-1}]]]]] (* Harvey P. Dale, Sep 20 2014 *)
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PROG
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(PARI) {a(n)=(5^n/n!^2)*prod(k=0, n-1, (10*k+2)*(10*k+3))}
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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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