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 A185402 a(n) = C(2n,n) * (7^n/n!^2) * Product_{k=0..n-1} (7k+2)*(7k+5). 3
 1, 140, 79380, 62563200, 57288340200, 57169180452384, 60324072262534080, 66193973824733314560, 74770747698820830356700, 86365239335124673905181200, 101541339191092781603799640464 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..320 FORMULA Self-convolution of A185401: A185401(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+2)*(14k+5). a(n) ~ cos(3*Pi/14) * 2^(2*n) * 7^(3*n) / (Pi*n)^(3/2). - Vaclav Kotesovec, Oct 23 2020 EXAMPLE G.f.: A(x) = 1 + 140*x + 79380*x^2 + 62563200*x^3 +... A(x)^(1/2) = 1 + 70*x + 37240*x^2 + 28674800*x^3 +...+ A185401(n)*x^n +... MATHEMATICA Table[Binomial[2n, n] 7^n/(n!)^2 Product[(7k+2)(7k+5), {k, 0, n-1}], {n, 0, 10}] (* Harvey P. Dale, May 10 2012 *) PROG (PARI) {a(n)=(2*n)!/n!^2*(7^n/n!^2)*prod(k=0, n-1, (7*k+2)*(7*k+5))} CROSSREFS Cf. A184896, A185401, A185404. Sequence in context: A189552 A181238 A211420 * A216729 A350614 A058939 Adjacent sequences: A185399 A185400 A185401 * A185403 A185404 A185405 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 26 2011 STATUS approved

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Last modified December 9 11:21 EST 2022. Contains 358700 sequences. (Running on oeis4.)