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A052337
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Number of partitions into at most a(1) copies of 1, a(2) copies of 2, ...
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2
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1, 1, 1, 2, 2, 3, 5, 6, 8, 10, 13, 17, 21, 27, 34, 42, 53, 65, 80, 98, 119, 146, 177, 213, 258, 309, 370, 443, 528, 628, 746, 883, 1044, 1231, 1449, 1703, 1997, 2338, 2734, 3190, 3718, 4325, 5025, 5830, 6754, 7816, 9032, 10422, 12016, 13832, 15907, 18274
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OFFSET
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0,4
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LINKS
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FORMULA
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E.g.f. satisfies A(x) = Product_{i>=1} (1-x^(a(i)*(i+1)))/(1-x^i).
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1), j=0..min(n/i, a(i)))))
end:
a:= n-> `if`(n=0, 0, 1)+b(n, n-1):
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i j, i - 1], {j, 0, Min[n/i, a[i]]}]]];
a[n_] := If[n == 0, 0, 1] + b[n, n - 1];
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CROSSREFS
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KEYWORD
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nonn,eigen
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AUTHOR
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STATUS
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approved
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