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A032154
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Number of ways to partition n elements into pie slices of different odd sizes.
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1
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1, 1, 0, 1, 1, 1, 1, 1, 2, 3, 2, 3, 3, 5, 3, 7, 10, 9, 10, 11, 17, 15, 23, 17, 36, 45, 42, 49, 61, 77, 73, 105, 98, 159, 116, 211, 267, 289, 291, 367, 454, 493, 604, 619, 893, 795, 1175, 969, 1716, 1937, 2124, 2185, 2917, 3225, 3697, 4289, 4862, 6147
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OFFSET
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0,9
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LINKS
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FORMULA
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"CGK" (necklace, element, unlabeled) transform of 1, 0, 1, 0, ... (odds).
G.f.: 1 + Sum_{k>=1} (k-1)! * x^(k^2) / (Product_{j=1..k} 1-x^(2*j)). - _Andrew Howroyd_, Sep 13 2018
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PROG
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(PARI) seq(n)=[subst(serlaplace(p/y), y, 1) | p <- Vec(y-1+prod(k=1, ceil(n/2), 1 + x^(2*k-1)*y + O(x*x^n)))] \\ _Andrew Howroyd_, Sep 13 2018
(PARI) seq(n)={Vec(1 + sum(k=1, sqrtint(n), my(r=k^2); (k-1)! * x^r / prod(j=1, k, 1 - x^(2*j) + O(x*x^(n-r)))))} \\ _Andrew Howroyd_, Sep 13 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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_Christian G. Bower_
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EXTENSIONS
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a(0)=1 prepended by _Andrew Howroyd_, Sep 13 2018
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STATUS
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approved
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