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 A128418 a(n) = Sum_{k=0..n} 2^(n-k)*C(2n,n-k). 3
 1, 5, 33, 233, 1697, 12585, 94449, 714873, 5445441, 41687369, 320420753, 2471008281, 19108837601, 148123058153, 1150532419377, 8952614975673, 69772391628417, 544532315255433, 4255064364533457, 33287174505889113, 260669265451935777, 2043172307192457513, 16028314647309873777 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums of number triangle A128417. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA G.f.: 8*x/(sqrt(1-8*x)*(sqrt(1-8*x)+12*x-1)); Conjecture: n^2*a(n)+(12+4*n-17*n^2)*a(n-1) +36*(n+1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Nov 05 2012 a(n) ~ 2^(3*n+1) / sqrt(Pi*n). - Vaclav Kotesovec, Feb 03 2014 MATHEMATICA Table[Sum[2^(n-k) Binomial[2n, n-k], {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Jan 06 2013 *) PROG (PARI) x='x +O('x^50); Vec(8*x/(sqrt(1-8*x)*(sqrt(1-8*x)+12*x-1))) \\ G. C. Greubel, Feb 09 2017 CROSSREFS Sequence in context: A083076 A361237 A162816 * A335119 A284733 A001887 Adjacent sequences: A128415 A128416 A128417 * A128419 A128420 A128421 KEYWORD easy,nonn AUTHOR Paul Barry, Mar 02 2007 STATUS approved

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Last modified November 29 13:49 EST 2023. Contains 367445 sequences. (Running on oeis4.)