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1, 2, 8, 21, 60, 133, 330, 675, 1474, 2910, 5838, 10920, 20944, 37673, 68580, 120384, 211365, 359964, 614845, 1022630, 1701678, 2776752, 4517016, 7232565, 11557350, 18201568, 28579152, 44373420, 68634280, 105109125, 160436916, 242692582, 365853180, 547346709
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) ~ exp(2*sqrt(2*n/3)*Pi)/(8*sqrt(6)*Pi*n^(3/2)) * (1 + (5*Pi/(12*sqrt(6)) - sqrt(3/2)/Pi)/sqrt(n) + (13*Pi^2/1728 - 19/48)/n). - Vaclav Kotesovec, Nov 04 2016
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EXAMPLE
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a(4) = 60 = sum of row 4 terms of row 4 in triangle A143228: (5 + 5 + 10 + 15 + 25).
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MATHEMATICA
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A143229[n_]:= PartitionsP[n]*Sum[PartitionsP[k], {k, 0, n}];
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PROG
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(Magma)
A143229:= func< n | NumberOfPartitions(n)*(&+[NumberOfPartitions(k): k in [0..n]]) >;
(SageMath)
def p(n): return number_of_partitions(n) # A000041
def A143229(n): return p(n)*sum(p(k) for k in range(n+1))
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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