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A107095
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G.f. satisfies: A(A(x)) = (1+x)^2*A(x).
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2
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0, 1, 2, -3, 18, -150, 1518, -17541, 223782, -3087948, 45470022, -707810715, 11569008816, -197540043324, 3509923686678, -64697804055675, 1234127209128306, -24312707152663590, 493834352052852738, -10327320248199824889, 222086739445484152590
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..20.
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FORMULA
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G.f. A(x) = G(x)^2/x where G(x) is g.f. of A107096.
a(n)=T(n,1), T(n,m)=sum(i=1..n-m, binomial(2*m,i)*T(n-i,m))-sum(k=m+1..n-1, T(n,k)*T(k,m)), n>m, T(n,n)=1. [Vladimir Kruchinin May 03 2012]
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PROG
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(PARI) {a(n)=local(A, B, F); if(n<1, 0, F=x+2*x^2+x*O(x^n); A=F; for(j=0, n, for(i=0, j, B=serreverse(A); A=(A+subst(B, x, A*(1+x)^2))/2); A=round(A)); polcoeff(A, n, x))}
(Maxima) T(n, m):=if n=m then 1 else sum(binomial(2*m, i)*T(n-i, m), i, 1, n-m)-sum(T(n, k)*T(k, m), k, m+1, n-1); makelist(T(n, 1), n, 1, 10); [Vladimir Kruchinin May 03 2012]
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CROSSREFS
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Cf. A107096.
Sequence in context: A184719 A076016 A226961 * A102939 A073983 A230602
Adjacent sequences: A107092 A107093 A107094 * A107096 A107097 A107098
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna, May 12 2005
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STATUS
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approved
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