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 A088221 Coefficient of x^n in g.f.^n is A000698(n+1). 1
 1, 2, 3, 10, 63, 558, 6226, 82836, 1272555, 22103638, 427715118, 9118752300, 212335628550, 5362040637900, 145970732893284, 4261945511044520, 132868133756374707, 4405535689300995942, 154819142574597555670 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..250 Ali Assem Mahmoud, On the Asymptotics of Connected Chord Diagrams, University of Waterloo (Ontario, Canada 2019). Ali Assem Mahmoud and Karen Yeats, Connected Chord Diagrams and the Combinatorics of Asymptotic Expansions, arXiv:2010.06550 [math.CO], 2020. FORMULA a(n) = Sum_{j=1..n-1} (4*j-1)*A000699(j)*A000699(n-j), with a(0)=1, a(1)=2. - G. C. Greubel, Feb 08 2020 MAPLE c:= proc(n) option remember; if n=1 then 1 else (n-1)*add( c(j)*c(n-j), j=1..n-1) fi; end: a:= proc(n) option remember; if n<2 then n+1 else add( (4*j-1)*c(j)*c(n-j), j=1..n-1) fi; end; seq(a(n), n=0..20); # G. C. Greubel, Feb 08 2020 MATHEMATICA c[n_]:= c[n]= If[n==1, 1, (n-1)*Sum[c[j]*c[n-j], {j, n-1}]]; a[n_]:= If[n<2, n+1, Sum[(4*j-1)*c[j]*c[n-j], {j, n-1}]]; Table[a[n], {n, 0, 20}] (* G. C. Greubel, Feb 08 2020 *) PROG (Sage) @CachedFunction def c(n): if (n==1): return 1 else: return (n-1)*sum( c(j)*c(n-j) for j in (1..n-1) ) def a(n): if (n<2): return n+1 else: return sum( (4*j-1)*c(j)*c(n-j) for j in (1..n-1) ) [a(n) for n in (0..20)] # G. C. Greubel, Feb 08 2020 CROSSREFS Cf. A000698, A000699. Sequence in context: A066526 A093856 A173097 * A206296 A124923 A291935 Adjacent sequences: A088218 A088219 A088220 * A088222 A088223 A088224 KEYWORD nonn AUTHOR Michael Somos, Sep 24 2003 STATUS approved

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Last modified March 29 14:32 EDT 2023. Contains 361599 sequences. (Running on oeis4.)