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 A184891 a(n) = (5^n/n!^2) * Product_{k=0..n-1} (10k+1)*(10k+4). 6
 1, 20, 3850, 1078000, 355066250, 128107903000, 49001272897500, 19520507080800000, 8012558140822125000, 3365274419145292500000, 1439327869068441602250000, 624739666805574817770000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..100 FORMULA 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). EXAMPLE 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 +... MATHEMATICA 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 *) PROG (PARI) {a(n)=(5^n/n!^2)*prod(k=0, n-1, (10*k+1)*(10*k+4))} CROSSREFS Cf. A184892; variants: A184424, A178529, A092870, A184895, A184897. Sequence in context: A225989 A332265 A177323 * A279297 A079759 A109894 Adjacent sequences: A184888 A184889 A184890 * A184892 A184893 A184894 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 25 2011 STATUS approved

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Last modified July 13 23:31 EDT 2024. Contains 374290 sequences. (Running on oeis4.)