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A190822
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G.f. satisfies: A(x) = Product_{n>=1} (1+x^n)*(1+x^(2n)*A(x)).
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3
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1, 1, 2, 4, 7, 14, 27, 53, 104, 208, 415, 836, 1690, 3434, 7004, 14342, 29460, 60707, 125443, 259883, 539689, 1123226, 2342493, 4894590, 10245321, 21481047, 45108768, 94863801, 199772929, 421245065, 889331420, 1879723964, 3977402460, 8424718846
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..33.
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FORMULA
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G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^(n*(n+1)/2)*Product_{k=1..n} (1+x^k*A(x))/(1-x^k) due to a Lebesgue identity.
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EXAMPLE
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G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 7*x^4 + 14*x^5 + 27*x^6 +...
G.f.: A(x) = (1+x)*(1+x^2*A(x))* (1+x^2)*(1+x^4*A(x))* (1+x^3)*(1+x^6*A(x))*...
G.f.: A(x) = 1 + x*(1+x*A(x))/(1-x) + x^3*(1+x*A(x))*(1+x^2*A(x))/((1-x)*(1-x^2)) + x^6*(1+x*A(x))*(1+x^2*A(x))*(1+x^3*A(x))/((1-x)*(1-x^2)*(1-x^3)) +...
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=prod(m=1, n, (1+x^m)*(1+x^(2*m)*A+x*O(x^n)))); polcoeff(A, n)}
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, sqrtint(2*n), x^(m*(m+1)/2)*prod(k=1, m, (1+A*x^k)/(1-x^k+x*O(x^n))))); polcoeff(A, n)}
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CROSSREFS
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Cf. A145267.
Sequence in context: A108758 A018085 A167751 * A107949 A155099 A136322
Adjacent sequences: A190819 A190820 A190821 * A190823 A190824 A190825
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, May 21 2011
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STATUS
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approved
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