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 A112698 Partial sum of Catalan numbers A000108 multiplied by powers of 4. 1
 1, 5, 37, 357, 3941, 46949, 587621, 7616357, 101332837, 1375876965, 18987759461, 265554114405, 3755416368997, 53610591434597, 771525112379237, 11181285666076517, 163041321978836837, 2390321854565988197 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..300 FORMULA a(n) = Sum_{k=0,..,n} C(k)*4^k, n>=0, with C(n):=A000108(n). G.f.: c(4*x)/(1-x), where c(x):=(1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers A000108. Recurrence: (n+1)*a(n) = (17*n-7)*a(n-1) - 8*(2*n-1)*a(n-2). - Vaclav Kotesovec, Oct 19 2012 a(n) ~ 16^(n+1)/(15*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012 MATHEMATICA CoefficientList[Series[(1-Sqrt[1-16*x])/(8*x)/(1-x), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *) PROG (PARI) x='x+O('x^50); Vec((1-sqrt(1-16*x))/(8*x*(1-x))) \\ G. C. Greubel, Mar 17 2017 CROSSREFS Fifth column (m=4) of triangle A112705. Sequence in context: A004208 A198077 A208813 * A234953 A025168 A084358 Adjacent sequences:  A112695 A112696 A112697 * A112699 A112700 A112701 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Oct 31 2005 STATUS approved

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Last modified January 23 11:04 EST 2019. Contains 319391 sequences. (Running on oeis4.)