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A225032
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Non-crossing, non-nesting, 6-colored set partitions.
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1
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1, 7, 55, 493, 5029, 57379, 716443, 9604345, 136236937, 2022864031, 31180099711, 495615409957, 8079827006125, 134488017925243, 2276945808434659, 39088515241450609, 678651272689389073, 11890942901283331255, 209891714523969067207, 3727004974842239659741
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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.: (1-56*x+1203*x^2-12364*x^3+60675*x^4-113540*x^5+x^6)/ (1-63*x+1589*x^2-20515*x^3+142915*x^4-509549*x^5+727767*x^6-x^7).
a(n) = 63*a(n-1) - 1589*a(n-2) + 20515*a(n-3) - 142915*a(n-4) + 509549*a(n-5) - 727767*a(n-6) + a(n-7) for n>6. - Colin Barker, Jun 22 2019
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EXAMPLE
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For n=2, a(2)=55 is the number of non-crossing, non-nesting set partitions on 3 elements with 6 possible arc colors.
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PROG
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(PARI) Vec((1 - 56*x + 1203*x^2 - 12364*x^3 + 60675*x^4 - 113540*x^5 + x^6) / (1 - 63*x + 1589*x^2 - 20515*x^3 + 142915*x^4 - 509549*x^5 + 727767*x^6 - x^7) + O(x^40)) \\ Colin Barker, Jun 22 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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