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A220892
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G.f.: (1+8*x+22*x^2+8*x^3+x^4)/(1-x)^6.
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4
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1, 14, 91, 364, 1085, 2666, 5719, 11096, 19929, 33670, 54131, 83524, 124501, 180194, 254255, 350896, 474929, 631806, 827659, 1069340, 1364461, 1721434, 2149511, 2658824, 3260425, 3966326, 4789539, 5744116, 6845189, 8109010, 9552991, 11195744, 13057121, 15158254, 17521595, 20170956, 23131549
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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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a(n) = (n+1)*(n^2+3*n+3)*(n^2+n+1)/3. [Colin Barker, Jan 03 2013]
The formula is simpler if the offset is 1 rather than 0. For a(n) = b*(1+b^2+b^4)/3, b >= 1. - N. J. A. Sloane, Nov 12 2019
E.g.f.: exp(x)*(3 + 39*x + 96*x^2 + 66*x^3 + 15*x^4 + x^5)/3. - Stefano Spezia, Dec 22 2021
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MATHEMATICA
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CoefficientList[Series[(1+8x+22x^2+8x^3+x^4)/(1-x)^6, {x, 0, 40}], x] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 14, 91, 364, 1085, 2666}, 40] (* Harvey P. Dale, Jan 11 2020 *)
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PROG
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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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