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A327623
Number of parts in all n-times partitions of n into distinct parts.
3
0, 1, 1, 7, 27, 121, 553, 3865, 24625, 202954, 1519540, 14193455, 132441998, 1381539355, 14096067555, 168745220585, 1961128020387, 25473872598375, 324797436024684, 4647784901400988, 65394584337577858, 1012005650484163962, 15285115573675197704
OFFSET
0,4
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, [1, 0],
`if`(k=0, [1, 1], `if`(i*(i+1)/2<n, 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-1), k)))(b(i$2, k-1)))))
end:
a:= n-> b(n$3)[2]:
seq(a(n), n=0..23);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = With[{}, If[n == 0, Return[{1, 0}]]; If[k == 0, Return[{1, 1}]]; If[i (i + 1)/2 < n, Return[{0, 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 - 1], k]]][b[i, i, k - 1]]];
a[n_] := b[n, n, n][[2]];
a /@ Range[0, 23] (* Jean-François Alcover, Dec 09 2020, after Alois P. Heinz *)
CROSSREFS
Main diagonal of A327622.
Cf. A327619.
Sequence in context: A249184 A118101 A201380 * A269070 A147996 A267365
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 19 2019
STATUS
approved