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Search: id:A158099
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| A158099 |
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Euler transform of square powers of 2: [2,2^4,2^9,...,2^(n^2),...]. |
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+0
2
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| 1, 2, 19, 548, 66749, 33695574, 68787981855, 563088066184424, 18447871299903970005, 2417888543453357864445634, 1267655436282309648681395304255, 2658458526916981532120588021462151100
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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G.f.: A(x) = 1/Product_{n>=1} (1 - x^n)^(2^(n^2)).
G.f.: exp( Sum_{n>=1} L(n)*x^n/n ) where L(n) = Sum_{d|n} d*2^(d^2). [From Paul D. Hanna (pauldhanna(AT)juno.com), Oct 18 2009]
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EXAMPLE
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G.f.: A(x) = 1 + 2*x + 19*x^2 + 548*x^3 + 66749*x^4 +...
A(x) = 1/[(1-x)^2*(1-x^2)^(2^4)*(1-x^3)^(2^9)*(1-x^4)^(2^16)*...].
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PROGRAM
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(PARI) a(n)=polcoeff(1/prod(k=1, n, (1-x^k+x*O(x^n))^(2^(k^2))), n)
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sumdiv(m, d, d*2^(d^2))*x^m/m)+x*O(x^n)), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Oct 18 2009]
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CROSSREFS
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Cf. A002416, A034899, A158098.
Sequence in context: A110818 A155927 A120420 this_sequence A015204 A086976 A118189
Adjacent sequences: A158096 A158097 A158098 this_sequence A158100 A158101 A158102
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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 20 2009
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