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A120915
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G.f. satisfies: A(x) = C(2x)^2 * A(x^3*C(2x)^4), where C(x) is the g.f. of the Catalan numbers (A000108).
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4
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1, 4, 20, 116, 720, 4656, 30996, 210896, 1459536, 10239796, 72651184, 520328112, 3756512912, 27307671040, 199705789248, 1468209751856, 10844681408064, 80437588353600, 598867568439828, 4473784063109904, 33524058847464912
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Column 0 of triangle A120914 (cascadence of (1+2x)^2).
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EXAMPLE
| A(x) = 1 + 4*x + 20*x^2 + 116*x^3 + 720*x^4 + 4656*x^5 + 30996*x^6 +...
= C(2x)^2 * A(x^3*C(2x)^4) where
C(2x) = 1 + 2*x + 8*x^2 + 40*x^3 + 224*x^4 + 1344*x^5 + 8448*x^6 +...
and C(x) is g.f. of the Catalan numbers (A000108): C(x) = 1 + x*C(x)^2.
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PROG
| (PARI) {a(n)=local(A=1+x, C=(1/x*serreverse(x/(1+4*x+4*x^2+x*O(x^n))))^(1/2)); for(i=0, n, A=C^2*subst(A, x, x^3*C^4 +x*O(x^n))); polcoeff(A, n, x)}
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CROSSREFS
| Cf. A120914, A120916 (square-root), A120917, A120918; A000108; variants: A092684, A092687, A120895, A120899, A120920.
Sequence in context: A077445 A085458 A085456 * A165311 A100328 A082298
Adjacent sequences: A120912 A120913 A120914 * A120916 A120917 A120918
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jul 17 2006
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