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Search: id:A158097
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| A158097 |
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G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)*x^n/(1 - 2^(n^2)*x^n)/n ). |
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+0
3
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| 1, 2, 14, 204, 16982, 6746636, 11467009772, 80444425963128, 2306004014991374374, 268654794950955551450892, 126765597355485863873077402788, 241678070949320869650125781001909864
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Compare to g.f. of the partition numbers A000041:
exp( Sum_{n>=1} x^n/(1 - x^n)/n ) = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 +...
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EXAMPLE
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G.f.: A(x) = 1 + 2*x + 14*x^2 + 204*x^3 + 16982*x^4 + 6746636*x^5 +...
log(A(x)) = 2*x + 24*x^2/2 + 536*x^3/3 + 66112*x^4/4 + 33554592*x^5/5 +...
log(A(x)) = 2*x/(1-2*x) + 2^4*x^2/(1-2^4*x^2)/2 + 2^9*x^3/(1-2^9*x^3)/3 +...
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PROGRAM
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(PARI) {a(n)=if(n==0, 1, polcoeff(exp(sum(k=1, n, (2^k*x)^k/(1-(2^k*x)^k +x*O(x^n))/k)), n))}
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CROSSREFS
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Cf. A158096, A155200.
Sequence in context: A123543 A054652 A122647 this_sequence A136550 A068369 A034405
Adjacent sequences: A158094 A158095 A158096 this_sequence A158098 A158099 A158100
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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), Mar 26 2009
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