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A327619
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Number of parts in all n-times partitions of n.
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4
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0, 1, 5, 25, 219, 1596, 19844, 208377, 3394835, 46799236, 886886076, 15668835975, 366602236558, 7582277939549, 199035634246870, 4962275379320665, 150339081311823341, 4214812414260868163, 141823733752997729872, 4533014863242019822308, 169587948261109794026999
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OFFSET
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0,3
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LINKS
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EXAMPLE
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a(2) = 5: 2, 11, 1|1.
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MAPLE
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b:= proc(n, i, k) option remember; `if`(n=0, [1, 0],
`if`(k=0, [1, 1], `if`(i<2, 0, b(n, i-1, k))+
(h-> (f-> f +[0, f[1]*h[2]/h[1]])(h[1]*
b(n-i, min(n-i, i), k)))(b(i$2, k-1))))
end:
a:= n-> b(n$3)[2]:
seq(a(n), n=0..21);
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MATHEMATICA
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b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1, 0}, If[k == 0, {1, 1}, If[i < 2, 0, b[n, i - 1, k]] + Function[h, Function[f, f + {0, f[[1]] h[[2]]/ h[[1]]}][h[[1]] b[n - i, Min[n - i, i], k]]][b[i, i, k - 1]]]];
a[n_] := b[n, n, n][[2]];
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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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