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A274252
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Number of partitions of n^5 into at most three parts.
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5
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1, 1, 102, 5043, 87894, 815365, 5042737, 23548008, 89494870, 290594892, 833383334, 2161532576, 5159904769, 11488393301, 24104823494, 48054578907, 91626493270, 168000201633, 297539880337, 510923426200, 853334933334, 1389992123568, 2213329476102, 3452212485976
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OFFSET
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0,3
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
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FORMULA
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Coefficient of x^(n^5) in 1/((1-x)*(1-x^2)*(1-x^3)).
G.f.: (1 -8*x +128*x^2 +4084*x^3 +46100*x^4 +193094*x^5 +407528*x^6 +512642*x^7 +407381*x^8 +193090*x^9 +46120*x^10 +4170*x^11 +70*x^12) / ((1 -x)^11*(1 +x)*(1 +x +x^2)).
a(n) = A001399(n^5) = round((n^5+3)^2/12). - Alois P. Heinz, Jun 16 2016
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PROG
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(PARI)
\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)).
b(n) = round(real((47+9*(-1)^n + 8*exp(-2/3*I*n*Pi) + 8*exp((2*I*n*Pi)/3) + 36*n+6*n^2)/72))
vector(50, n, n--; b(n^5))
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CROSSREFS
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A subsequence of A001399.
Cf. A274250 (n^2), A274251 (n^3), A274253 (n^7), A274254 (n^11).
Sequence in context: A203401 A217331 A284448 * A303993 A030512 A097725
Adjacent sequences: A274249 A274250 A274251 * A274253 A274254 A274255
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KEYWORD
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nonn
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AUTHOR
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Colin Barker, Jun 16 2016
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STATUS
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approved
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