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Search: id:A120956
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| A120956 |
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G.f. A(x) satisfies x/series_reversion(x*A(x)) = (A(x) + 1+x)/2. |
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+0
2
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| 1, 1, 2, 8, 50, 412, 4120, 47840, 628130, 9164600, 146786980, 2557718352, 48147082520, 973612557504, 21050077835440, 484637221115520, 11839623684281890, 305949448095405252, 8339153054042801704
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The g.f. for A120955 = x/series_reversion(x*A(x)) = (A(x) + 1+x)/2.
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FORMULA
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a(n) = 2*A120955(n) for n>=2. G.f. A(x) satisfies: A( 2x/(A(x) + 1+x) ) = (A(x) + 1+x)/2. G.f. A(x) satisfies: A(x) = F(x*A(x)) and F(x) = A(x/F(x)) where F(x) = g.f. of A120955.
G.f. satisfies: A(x) = (1 + A(x*A(x)) )/(2-x).
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EXAMPLE
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A(x) = 1 + x + 2*x^2 + 8*x^3 + 50*x^4 + 412*x^5 + 4120*x^6 +...
The g.f. of A120955 is:
x/series_reversion(x*A(x)) = 1 + x + x^2 + 4*x^3 + 25*x^4 + 206*x^5 +...
Compare terms to see that A120955(n) = a(n)/2 for n>=2.
A(x*A(x)) = 1 + x + 3*x^2 + 14*x^3 + 92*x^4 + 774*x^5 +...
A(x)*(2-x) = 2 + x + 3*x^2 + 14*x^3 + 92*x^4 + 774*x^5 +...
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PROGRAM
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(PARI) {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, t); A[ #A]=subst(Vec(serreverse(x/Ser(A)))[ #A], t, 0)); Vec(serreverse(x/Ser(A)))[n+1]}
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CROSSREFS
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Cf. A120955.
Sequence in context: A027047 A034491 A121677 this_sequence A000557 A002801 A089104
Adjacent sequences: A120953 A120954 A120955 this_sequence A120957 A120958 A120959
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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 19 2006
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