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A127632
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Expansion of 1/(1 - x*c(x) * c(x*c(x))), where c(x) is the g.f. of A000108.
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7
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1, 1, 3, 11, 44, 185, 804, 3579, 16229, 74690, 347984, 1638169, 7780876, 37245028, 179503340, 870374211, 4243141332, 20786340271, 102275718924, 505235129250, 2504876652190, 12459922302900, 62167152967680, 311040862133625
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Row sums of number triangle A127631. Hankel transform appears to be A075845.
Catalan transform of Catalan numbers . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 20 2007
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FORMULA
| a(n) = A127714(n+1,2n+1).
G.f. A(x) satisfies 0 = 1 - A(x) + A(x)^2 * x * c(x) where c(x) is the g.f. of A000108.
G.f.: 2/(1 + sqrt( 2 * sqrt(1 -4*x) - 1)). - Michael Somos May 04 2007
a(n) = Sum_{k, 0<=k<=n}A106566(n,k)*A000108(k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 20 2007
a(n) = sum(m=1..n, m*sum(k=m..n, binomial(2*k-m-1,k-1)*binomial(2*n-k-1,n-1)))/n, a(0)=1. [From Vladimir Kruchinin, Oct 08 2011]
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PROG
| (PARI) {a(n)= if(n<1, n==0, polcoeff( serreverse( x*(1-x)^3*(1-x^3)/(1-x^2)^4 +x*O(x^n) ), n))} /* Michael Somos May 04 2007 */
(PARI) {a(n)= local(A); if(n<1, n==0, A= serreverse( x-x^2 +x*O(x^n) ); polcoeff( 1/(1 - subst(A, x, A)), n))} /* Michael Somos May 04 2007 */
(Maxima)
a(n):=if n=0 then 1 else sum(m*sum(binomial(2*k-m-1, k-1)*binomial(2*n-k-1, n-1), k, m, n), m, 1, n)/n; [From Vladimir Kruchinin, Oct 8 2011]
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CROSSREFS
| Cf. A127714.
Sequence in context: A132840 A091200 A151105 * A061706 A167012 A167013
Adjacent sequences: A127629 A127630 A127631 * A127633 A127634 A127635
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 20 2007, Jan 25 2007
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