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Search: id:A124541
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| A124541 |
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G.f.: A(x) = R_2(x)/R_1(x), where R_2(x) and R_1(x) are the g.f.s of row 2 (A124542) and row 1 (A124531), respectively, of table A124540. |
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1
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| 1, 1, 4, 15, 63, 295, 1502, 8167, 46873, 281672, 1761798, 11418480, 76415644, 526594846, 3728435747, 27073765165, 201325681384, 1531247489953, 11899881220174, 94409837555587, 764105555574024, 6304959856949278
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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In table A124540, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = [ Sum_{k>=0} y^k*R_k(y)^n ]^n for n>=0.
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EXAMPLE
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G.f.: A(x) = R_2(x)/R_1(x), where row g.f.s are:
R_2(x) = 1 + 2x + 7x^2 + 26x^3 + 107x^4 + 486x^5 + 2398x^6 +..., and
R_1(x) = 1 + x + 2x^2 + 5x^3 + 16x^4 + 62x^5 + 274x^6 +..., so that
A(x) = 1 + x + 4*x^2 + 15*x^3 + 63*x^4 + 295*x^5 + 1502*x^6 +...
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PROGRAM
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(PARI) {a(n)=local(R); R=vector(n+3, r, vector(n+3, c, 1)); for(i=0, n+2, for(r=0, n+2, R[r+1]=Vec(sum(c=0, n, x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); Vec(Ser(R[3])^2/Ser(R[2])+O(x^(n+1)))[n+1]}
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CROSSREFS
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Cf. A124540 (table); rows: A124531, A124542, A124543, A124544, A124545, A124546.
Sequence in context: A007167 A036728 A027216 this_sequence A134597 A007526 A097422
Adjacent sequences: A124538 A124539 A124540 this_sequence A124542 A124543 A124544
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Nov 05 2006
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