A327619 Number of parts in all n-times partitions of n.

0, 1, 5, 25, 219, 1596, 19844, 208377, 3394835, 46799236, 886886076, 15668835975, 366602236558, 7582277939549, 199035634246870, 4962275379320665, 150339081311823341, 4214812414260868163, 141823733752997729872, 4533014863242019822308, 169587948261109794026999

Offset

0,3

Links

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

Wikipedia, Partition (number theory)

Example

a(2) = 5: 2, 11, 1|1.

Maple

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);

Mathematica

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]];
a /@ Range[0, 21] (* Jean-François Alcover, May 01 2020, after Maple *)

Crossrefs

Main diagonal of A327618.

Cf. A306187, A327623.

Sequence in context: A080632 A245166 A144575 * A005452 A061839 A143600

Adjacent sequences: A327616 A327617 A327618 * A327620 A327621 A327622

Keyword

nonn

Author

Alois P. Heinz, Sep 19 2019

Status

approved