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A184891
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a(n) = (5^n/n!^2) * Product_{k=0..n-1} (10k+1)*(10k+4).
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6
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1, 20, 3850, 1078000, 355066250, 128107903000, 49001272897500, 19520507080800000, 8012558140822125000, 3365274419145292500000, 1439327869068441602250000, 624739666805574817770000000
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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) = A184892(n) where
. A184892(n) = C(2n,n) * (5^n/n!^2)*Product_{k=0..n-1} (5k+1)*(5k+4).
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EXAMPLE
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G.f.: A(x) = 1 + 20*x + 3850*x^2 + 1078000*x^3 +...
A(x)^2 = 1 + 40*x + 8100*x^2 + 2310000*x^3 +...+ A184892(n)*x^n +...
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MATHEMATICA
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Table[5^n/(n!)^2 Product[(10k+1)(10k+4), {k, 0, n-1}], {n, 0, 20}] (* Harvey P. Dale, Feb 02 2012 *)
FullSimplify[Table[2^(2*n) * 5^(3*n) * Gamma[n+1/10] * Gamma[n+2/5] / (Gamma[2/5] * Gamma[1/10] * Gamma[n+1]^2), {n, 0, 15}]] (* Vaclav Kotesovec, Jul 03 2014 *)
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PROG
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(PARI) {a(n)=(5^n/n!^2)*prod(k=0, n-1, (10*k+1)*(10*k+4))}
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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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