A327590 Number of partitions in all twice partitions of n.

0, 1, 4, 10, 29, 63, 164, 339, 797, 1640, 3578, 7139, 15210, 29621, 60381, 117116, 232523, 442388, 863069, 1621560, 3105993, 5785525, 10894394, 20083143, 37434186, 68344449, 125774280, 228088127, 415668548, 747660318, 1351364816, 2413792653, 4327245170

Offset: 0

Author

Alois P. Heinz, Sep 17 2019

Keywords

• nonn

Examples

			a(3) = 10 = 1+1+1+2+2+3 counting the partitions in 3, 21, 111, 2|1, 11|1, 1|1|1.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A000041, A006128, A063834, A066633, A327552, A327553, A327554, A327594.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, 0, b(n, i-1)+
      (p-> p+[0, p[1]])(combinat[numbpart](i)*b(n-i, min(n-i, i)))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..42);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i<1, {0, 0}, b[n, i-1] + Function[p, p + {0, p[[1]]}][PartitionsP[i] b[n-i, Min[n-i, i]]]]];
a[n_] := b[n, n][[2]];
a /@ Range[0, 42] (* Jean-François Alcover, Dec 16 2020, after Alois P. Heinz *)