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A182805
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Number of 10-core partitions of n.
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2
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1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 32, 46, 57, 71, 85, 106, 121, 147, 165, 190, 242, 267, 302, 350, 400, 443, 511, 565, 638, 715, 774, 852, 964, 1038, 1135, 1253, 1372, 1482, 1650, 1785, 1878, 2098, 2234, 2411, 2625, 2819, 2963, 3249, 3393, 3600, 4004, 4181
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: Product_{i>=1} (1-x^(10*i))^10/(1-x^i).
Euler transform of period 10 sequence [1,1,1,1,1,1,1,1,1,-9,.. ].
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MAPLE
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with(numtheory): A:= proc(n, t) option remember; local d, j; `if`(n=0, 1, add(add(`if`(t=0 or irem(d, t)=0, d-d*t, d), d=divisors(j)) *A(n-j, t), j=1..n)/n) end: seq(A(n, 10), n=0..50);
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MATHEMATICA
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A[n_, t_]:= A[n, t] = Module[{d, j}, If[n == 0, 1, Sum[Sum[If[t == 0 || Mod[d, t] == 0, d - d t, d], {d, Divisors[j]}] A[n - j, t], {j, 1, n}]/n]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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