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A045823
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a(n)=sigma_3(2n+1).
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6
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1, 28, 126, 344, 757, 1332, 2198, 3528, 4914, 6860, 9632, 12168, 15751, 20440, 24390, 29792, 37296, 43344, 50654, 61544, 68922, 79508, 95382, 103824, 117993, 137592, 148878, 167832, 192080, 205380, 226982, 260408, 276948, 300764, 340704, 357912
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| Expansion of q^(-1) * ( E_4(q) - 9 * E_4(q^2) + 8 * E_4(q^4) ) / 240 in powers of q^2. - Michael Somos Nov 29 2007
Expansion of q^(-1) * (eta(q^2)^24 + eta(q)^16 * eta(q^4)^8) / (2 * eta(q)^8 * eta(q^2)^8) in powers of q^2. - Michael Somos Nov 29 2007
a(n) = b(2*n+1) where b(n) is multiplicative and b(2^e) = 0^e, b(p^e) = ((p^3)^(e+1) - 1) / (p^3 - 1) if p>2. - Michael Somos Nov 29 2007
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EXAMPLE
| q + 28*q^3 + 126*q^5 + 344*q^7 + 757*q^9 + 1332*q^11 + 2198*q^13 + ...
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PROG
| (PARI) {a(n) = if( n<0, 0, sigma(2 * n + 1, 3))} /* Michael Somos Nov 29 2007 */
(PARI) {a(n) = local(A); if( n<0, 0, n *= 2; A = x * O(x^n); polcoeff( (eta(x^2 + A)^24 + eta(x + A)^16 * eta(x^4 + A)^8) / (2 * eta(x + A)^8 * eta(x^2 + A)^8), n))} /* Michael Somos Nov 29 2007 */
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CROSSREFS
| A045819/2.
Bisection of A001158. Cf. A008438.
Sequence in context: A042536 A042538 A101095 * A044360 A044741 A184679
Adjacent sequences: A045820 A045821 A045822 * A045824 A045825 A045826
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 12 2003
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