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A335635
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Expansion of e.g.f. Product_{k>0} 1/(1 - sin(x)^k / k).
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4
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1, 1, 3, 10, 44, 215, 1252, 7992, 56024, 438341, 3672328, 32587366, 318586880, 3325053147, 35115462592, 407034567076, 5198294627456, 63965057355305, 824995119961984, 12611299833296898, 184189806819806720, 2590874864719588031, 44912343151409875456, 728583107189913021328, 11458864344772729650176
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OFFSET
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0,3
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COMMENTS
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a(30) is negative.
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LINKS
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FORMULA
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E.g.f.: exp( Sum_{i>0} Sum_{j>0} sin(x)^(i*j)/(i*j^i) ).
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MATHEMATICA
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max = 24; Range[0, max]! * CoefficientList[Series[Product[1/(1 - Sin[x]^k/k), {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Oct 03 2020 *)
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PROG
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(PARI) N=40; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, 1-sin(x)^k/k)))
(PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(sum(i=1, N, sum(j=1, N\i, sin(x)^(i*j)/(i*j^i))))))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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