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A260116
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G.f.: Sum_{n=-oo..+oo} (x + x^n)^n.
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5
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1, 3, 1, 2, 3, 5, 1, 5, 1, 9, 10, 6, 1, 16, 1, 8, 23, 27, 1, 25, 1, 24, 36, 12, 1, 95, 26, 14, 55, 52, 1, 77, 1, 131, 78, 18, 108, 207, 1, 20, 105, 303, 1, 135, 1, 190, 430, 24, 1, 697, 50, 236, 171, 315, 1, 307, 661, 606, 210, 30, 1, 1845, 1, 32, 591, 899, 1288, 727, 1, 717, 300, 1247, 1, 3256, 1, 38, 2626, 1010, 1387, 1652, 1, 3925, 487, 42, 1, 6681, 3741, 44, 465, 2379, 1
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: 1 + Sum_{n>=1} x^n*(1 + x^(n-1))^n + x^(n^2)/(1 + x^(n+1))^n.
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EXAMPLE
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G.f.: A(x) = 1 + 3*x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + x^6 + 5*x^7 + x^8 + 9*x^9 + 10*x^10 + 6*x^11 + x^12 + 16*x^13 + x^14 + 8*x^15 + 23*x^16 +...
where A(x) = 1 + P(x) + N(x) with
P(x) = (x+x) + (x+x^2)^2 + (x+x^3)^3 + (x+x^4)^4 + (x+x^5)^5 + (x+x^6)^6 + (x+x^7)^7 +...+ (x+x^n)^n +...
N(x) = 1/(x+1/x) + 1/(x+1/x^2)^2 + 1/(x+1/x^3)^3 + 1/(x+1/x^4)^4 + 1/(x+1/x^5)^5 +...+ 1/(x+1/x^n)^n +...
Explicitly,
P(x) = 2*x + x^2 + 3*x^3 + 2*x^4 + 4*x^5 + x^6 + 8*x^7 + x^8 + 7*x^9 + 7*x^10 + 7*x^11 + x^12 + 22*x^13 + x^14 + 9*x^15 + 17*x^16 +...
N(x) = x - x^3 + x^4 + x^5 - 3*x^7 + 2*x^9 + 3*x^10 - x^11 - 6*x^13 - x^15 + 6*x^16 + 7*x^17 - 7*x^19 - 13*x^21 + 7*x^22 - x^23 +...
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PROG
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(PARI) {a(n) = local(A=1); A = sum(k=-n, n, (x+x^k)^k +x*O(x^n)); polcoeff(A, n)}
for(n=0, 100, print1(a(n), ", "))
(PARI) {a(n) = local(A=1); A = 1 + sum(k=1, n, x^k*(1+x^(k-1))^k + x^(k^2)/(1+x^(k+1))^k +x*O(x^n)); polcoeff(A, n)}
for(n=0, 100, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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