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Search: id:A110448
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| 1, 1, 2, 3, 6, 8, 18, 23, 49, 73, 145, 194, 474, 611, 1331, 2027, 4393, 5919, 14736, 19415, 46487, 68504, 156618, 212055, 560380, 739165, 1833012, 2657837, 6513367, 8743208, 23649777, 31140300, 81276046, 114962333, 293600318, 391926154
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OFFSET
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0,3
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FORMULA
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G.f.: A(x) = Product_{n>=1} (1/x)*Series_Reversion( x/(1 + x^n) ); equivalently, G.f.: A(x) = Product_{n>=1} G(x^n,n) where G(x,n) = 1 + x*G(x,n)^n.
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EXAMPLE
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exp( Sum_{n>=1} A056045(n)/n*x^n ) =
exp(x + 3/2*x^2 + 4/3*x^3 + 11/4*x^4 + 6/5*x^5 +...)
= 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 8*x^5 + 18*x^6 +...
A(x) = 1/(1-x)*G000108(x^2)*G001764(x^3)*G002293(x^4)*G002294(x^5)*...
where the functions are g.f.s of well-known sequences:
G000108(x) = g.f. of A000108 = 1 + x*G000108(x)^2;
G001764(x) = g.f. of A001764 = 1 + x*G001764(x)^3;
G002293(x) = g.f. of A002293 = 1 + x*G002293(x)^4;
G002294(x) = g.f. of A002294 = 1 + x*G002294(x)^5 ; etc.
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PROGRAM
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(PARI) {a(n)=polcoeff(exp(x*Ser(vector(n, m, sumdiv(m, d, binomial(m, d))/m))+x*O(x^n)), n)}
(PARI) {a(n)=polcoeff(prod(m=1, n, 1/x*serreverse(x/(1+x^m +x*O(x^n)))), n)}
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CROSSREFS
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Cf. A056045.
Cf. A000108, A001764, A002293, A002294, A002295.
Sequence in context: A057574 A103065 A005508 this_sequence A064450 A130623 A072847
Adjacent sequences: A110445 A110446 A110447 this_sequence A110449 A110450 A110451
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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 20 2005, Nov 10 2007
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