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Search: id:A107590
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| A107590 |
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G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n*(n-1)/2). |
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+0
6
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| 1, 1, 1, 2, 5, 15, 50, 181, 698, 2837, 12062, 53374, 244923, 1162536, 5697119, 28786266, 149814059, 802436166, 4420515689, 25031466730, 145616087486, 869760092469, 5330945435272, 33508699787635, 215863606818041
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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G.f. A(x) = x/series-reversion(x*G107591(x)) and thus A(x) = G107591(x/A(x)) where G107591(x) is the g.f. of A107591. G.f. A(x)^2 = x/series-reversion(x*G107592(x)^2) and thus A(x) = G107592(x/A(x)^2) where G107592(x) is the g.f. of A107592.
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EXAMPLE
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A = 1 + x + x^2*A^1 + x^3*A^3 + x^4*A^6 + x^5*A^10 +...
= 1 + x + (x^2 + x^3 + x^4 + 2*x^5 + 5*x^6 + 15*x^7 +...)
+ (x^3 + 3*x^4 + 6*x^5 + 13*x^6 + 33*x^7 +...)
+ (x^4 + 6*x^5 + 21*x^6 + 62*x^7 +...)
+ (x^5 + 10*x^6 + 55*x^7 +...) +...
= 1 + x + x^2 + 2*x^3 + 5*x^4 + 15*x^5 + 50*x^6 + 181*x^7 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*A^(j*(j-1)/2)+x*O(x^n))); polcoeff(A, n)}
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CROSSREFS
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Cf. A107591, A107592.
Sequence in context: A024718 A007853 A060049 this_sequence A007581 A124303 A073525
Adjacent sequences: A107587 A107588 A107589 this_sequence A107591 A107592 A107593
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KEYWORD
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eigen,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 17 2005
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