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Search: id:A120900
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| A120900 |
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G.f. satisfies: A(x) = C(x)*A(x^3*C(x)^4), where C(x) is the g.f. of the Catalan numbers (A000108). |
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4
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| 1, 1, 2, 6, 19, 62, 209, 722, 2539, 9054, 32654, 118876, 436171, 1611067, 5984943, 22344455, 83786875, 315397144, 1191324649, 4513742858, 17149228138, 65318912291, 249356597492, 953902701488, 3656057618727, 14037222220896
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Self-convolution equals A120899, which equals column 0 of triangle A120898 (cascadence of 1+2x+x^2).
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EXAMPLE
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A(x) = 1 + x + 2*x^2 + 6*x^3 + 19*x^4 + 62*x^5 + 209*x^6 + 722*x^7 +...
= C(x) * A(x^3*C(x)^4) where
C(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +...
is the g.f. of the Catalan numbers (A000108): C(x) = 1 + x*C(x)^2.
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PROGRAM
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(PARI) {a(n)=local(A=1+x, C=(1/x*serreverse(x/(1+2*x+x^2+x*O(x^n))))^(1/2)); for(i=0, n, A=C*subst(A, x, x^3*C^4 +x*O(x^n))); polcoeff(A, n, x)}
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CROSSREFS
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Cf. A120898, A120899, A000108.
Adjacent sequences: A120897 A120898 A120899 this_sequence A120901 A120902 A120903
Sequence in context: A033193 A071738 A026012 this_sequence A059712 A059713 A109262
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 14 2006
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