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 A029887 A sum over scaled A000531 related to Catalan numbers C(n). 6
 1, 11, 82, 515, 2934, 15694, 80324, 397923, 1922510, 9105690, 42438076, 195165646, 887516252, 3997537980, 17857602568, 79200753059, 349051186494, 1529735010658, 6670733733260, 28959032959962, 125209652884756, 539384745200516, 2315840230811832, 9912689725127950 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Related to planar maps? - see A000184. - N. J. A. Sloane, Mar 11 2007 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 FORMULA a(n) = 4^n*sum(A000531(k+1)/4^k, k=0..n) = (2*n+1)*(2*n+3)*(2*n+5)*C(n)/3-(n+2)*2^(2*n+1); a(n)=4*a(n-1)+A000531(n+1). G.f. c(x)/(1-4*x)^(5/2) = (2-c(x))/(1-4*x)^3, where c(x) = g.f. for Catalan numbers; also convolution of Catalan numbers with A002802. G.f.: (4*x-1+sqrt(1-4*x))/(2*x*(1-4*x)^3). -  Vincenzo Librandi, Mar 14 2014 MATHEMATICA a[n_] := (2*n+1)*(2*n+3)*(2*n+5)*CatalanNumber[n]/3 - (n+2)*2^(2*n+1); Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Mar 12 2014 *) CoefficientList[Series[(4 x - 1 + Sqrt[1 - 4 x])/(2 x (1 - 4 x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 14 2014 *) PROG (MAGMA) [(2*n+1)*(2*n+3)*(2*n+5)*Catalan(n)/3 - (n+2)*2^(2*n+1): n in [0..30]]; // Vincenzo Librandi, Mar 14 2014 CROSSREFS Cf. A000184, A000531, A000108, A002802. Sequence in context: A197643 A261391 A211845 * A026871 A123367 A177142 Adjacent sequences:  A029884 A029885 A029886 * A029888 A029889 A029890 KEYWORD nonn AUTHOR EXTENSIONS More terms from Vincenzo Librandi, Mar 14 2014 STATUS approved

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Last modified July 25 13:59 EDT 2021. Contains 346290 sequences. (Running on oeis4.)