A327623 Number of parts in all n-times partitions of n into distinct parts.

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

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Wikipedia, Partition (number theory)

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

Adjacent sequences: A327620 A327621 A327622 * A327624 A327625 A327626

Keyword

nonn

Author

Alois P. Heinz, Sep 19 2019

Status

approved