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Search: id:A022577
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| A022577 |
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Expansion of Product (1+q^m)^12; m=1..inf. |
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+0
3
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| 1, 12, 78, 376, 1509, 5316, 16966, 50088, 138738, 364284, 913824, 2203368, 5130999, 11585208, 25444278, 54504160, 114133296, 234091152, 471062830, 931388232, 1811754522, 3471186596, 6556994502, 12222818640, 22502406793, 40944396120
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Euler transform of period 2 sequence [12, 0, ...]. - Michael Somos, Jul 16 2005
Expansion of q^(-1/2)(k/4)/(1-k^2) in powers of q. - Michael Somos Jul 16 2005
Expansion of q^(-1/2)(eta(q^2)/eta(q))^12 in powers of q. - Michael Somos, Jul 16 2005
Given g.f. A(x), then B(x)=(x*A(x^2))^2 satisfies 0=f(B(x), B(x^2)) where f(u, v)=(4096uv+48u+1)v-u^2 . - Michael Somos Jul 16 2005
G.f.: Product_{k>0} (1+x^k)^12.
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff( prod(k=1, n, 1+x^k, 1+x*O(x^n))^12, n)) /* Michael Somos Jul 16 2005 */
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^2+A)/eta(x+A))^12, n))} /* Michael Somos Jul 16 2005 */
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CROSSREFS
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A007096(4n+2)=8*a(n).
Sequence in context: A001288 A121665 A124863 this_sequence A030116 A035042 A061593
Adjacent sequences: A022574 A022575 A022576 this_sequence A022578 A022579 A022580
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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