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 A129366 a(n) = Sum_{k=0..floor(n/2)} C(n-k), where C(n) = A000108(n). 1
 1, 1, 3, 7, 21, 61, 193, 617, 2047, 6895, 23691, 82435, 290447, 1033215, 3707655, 13402071, 48759741, 178403101, 656041801, 2423300129, 8987420549, 33453670773, 124936234413, 467995789277, 1757899936601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Partial sums of (A129367 prefixed by an initial 1). LINKS Table of n, a(n) for n=0..24. FORMULA G.f.: (1/(1-x))*(c(x)-x*c(x^2)), where c(x) is the g.f. of A000108(n). G.f.: (sqrt(1-4*x^2)-sqrt(1-4*x))/(2*x*(1-x)). a(n) = Sum_{k=floor((n+1)/2)..n} C(k), where C(n) = A000108(n). Conjecture: +n*(12*n+35)*(n-1)*a(n) +(n-1)*(12*n^2-701*n+1236)*a(n-1) +2*(6*n^3-385*n^2+2285*n-3432)*a(n-2) +4*(-405*n^3+5313*n^2-19970*n+23175)*a(n-3) +8*(156*n^3-1724*n^2+5498*n-5175)*a(n-4) +16*(393*n^3-4981*n^2+20393*n-26820)*a(n-5) -32*(n-5)*(93*n-268)*(2*n-9)*a(n-6) = 0. - R. J. Mathar, Feb 05 2015 MATHEMATICA Table[Sum[CatalanNumber[k], {k, Floor[(n + 1)/2], n}], {n, 0, 30}] (* Wesley Ivan Hurt, Jun 18 2022 *) CROSSREFS Cf. A000108, A129367. Sequence in context: A005355 A182399 A025235 * A270049 A166358 A148670 Adjacent sequences: A129363 A129364 A129365 * A129367 A129368 A129369 KEYWORD easy,nonn AUTHOR Paul Barry, Apr 11 2007 STATUS approved

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Last modified September 22 14:29 EDT 2023. Contains 365531 sequences. (Running on oeis4.)