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Search: id:A145350
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| A145350 |
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G.f. satisfies: A(x/A(x)^2) = 1 + x*A(x). |
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2
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| 1, 1, 3, 18, 154, 1632, 20007, 273164, 4058556, 64628487, 1091488334, 19403175105, 361028420037, 7000932594042, 141010975529568, 2942134448306481, 63449975020918843, 1411787024678728344, 32360032648643379471
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f.: A(x) = 1 + x*G(x)^3 where G(x) = A(x*G(x)^2) and A(x) = G(x/A(x)^2).
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EXAMPLE
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G.f.: A(x) = 1 + x + 3*x^2 + 18*x^3 + 154*x^4 + 1632*x^5 +...
A(x)^2 = 1 + 2*x + 7*x^2 + 42*x^3 + 353*x^4 + 3680*x^5 + 44526*x^6+...
A(x/A(x)^2) = 1 + x + x^2 + 3*x^3 + 18*x^4 + 154*x^5 + 1632*x^6 +...
A(x) = 1 + x*G(x)^3 where G(x) = A(x*G(x)^2):
G(x) = 1 + x + 5*x^2 + 41*x^3 + 432*x^4 + 5329*x^5 + 73512*x^6 +...
G(x)^2 = 1 + 2*x + 11*x^2 + 92*x^3 + 971*x^4 + 11932*x^5 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x, G); for(i=0, n, G=(serreverse(x/(A+x*O(x^n))^2)/x)^(1/2); A=1+x*G^3); polcoeff(A, n)}
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CROSSREFS
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Cf. variants: A001764, A147664, A120972.
Sequence in context: A138420 A152409 A005412 this_sequence A107888 A138274 A060913
Adjacent sequences: A145347 A145348 A145349 this_sequence A145351 A145352 A145353
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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), Nov 12 2008
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