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

Author

Alois P. Heinz, Sep 19 2019

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300
• Wikipedia, Partition (number theory)

Crossrefs

Main diagonal of A327618.

Cf. A306187, A327623.

Programs

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 *)