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A137571
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Main diagonal of square array A137570.
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3
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1, 2, 10, 60, 397, 2802, 20710, 158428, 1244413, 9980220, 81394123, 672998498, 5628741195, 47535483498, 404790717079, 3471892750622, 29966295451511, 260080708564964, 2268416956569463, 19872441881999354, 174783803353387498
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A variant is A007857, the number of independent sets in rooted plane trees on n nodes.
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FORMULA
| G.f. A(x) = 1/(1 - x*C(x)*F(x)^2 - x*F(x)^3), where C(x) = 1 + xC(x)^2 is g.f. of Catalan numbers (A000108) and F(x) = 1 + xF(x)^4 is g.f. of A002293.
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EXAMPLE
| G.f.: A(x) = 1 + 2*x + 10*x^2 + 60*x^3 + 397*x^4 + 2802*x^5 +...;
A(x) = 1/(1 - x*C(x)*F(x)^2 - x*F(x)^3), where
C(x) = 1 + xC(x)^2 is g.f. of Catalan numbers (A000108):
[1, 1, 2, 5, 14, 42, 132, 429, 1430, ..., C(2n,n)/(n+1), ...] and
F(x) = 1 + xF(x)^4 is g.f. of A002293:
[1, 1, 4, 22, 140, 969, 7084, 53820, ..., C(4n,n)/(3n+1), ...].
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PROG
| (PARI) {a(n)=local(m=n+1, C, F, A); C=Ser(vector(m, r, binomial(2*r-2, r-1)/r)); F=Ser(vector(m, r, binomial(4*r-4, r-1)/(3*r-2))); A=1/(1-x*C*F^2-x*F^3); polcoeff(A+O(x^m), n, x)}
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CROSSREFS
| Cf. A137570, A137572, A137573; A007857 (variant); A000108, A002293.
Sequence in context: A114620 A173613 A004981 * A098616 A082042 A079856
Adjacent sequences: A137568 A137569 A137570 * A137572 A137573 A137574
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jan 27 2008
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