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A088221
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Coefficient of x^n in g.f.^n is A000698(n+1).
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1
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1, 2, 3, 10, 63, 558, 6226, 82836, 1272555, 22103638, 427715118, 9118752300, 212335628550, 5362040637900, 145970732893284, 4261945511044520, 132868133756374707, 4405535689300995942, 154819142574597555670
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OFFSET
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0,2
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LINKS
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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.
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A000698, A000699.
Sequence in context: A066526 A093856 A173097 * A206296 A124923 A291935
Adjacent sequences: A088218 A088219 A088220 * A088222 A088223 A088224
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Sep 24 2003
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STATUS
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approved
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