A327607 Number of parts in all twice partitions of n where the first partition is strict.

0, 1, 3, 11, 21, 58, 128, 276, 516, 1169, 2227, 4324, 8335, 15574, 29116, 55048, 97698, 176291, 323277, 563453, 1005089, 1770789, 3076868, 5293907, 9184885, 15668638, 26751095, 45517048, 76882920, 128738414, 217219751, 360525590, 599158211, 995474365

Offset: 0

Author

Alois P. Heinz, Sep 18 2019

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..4000

Crossrefs

Cf. A000009, A000041, A271619, A327552, A327594, A327605, A327608.

Programs

Maple

g:= proc(n) option remember; (p-> [p(n), add(p(n-j)*
      numtheory[tau](j), j=1..n)])(combinat[numbpart])
    end:
b:= proc(n, i) option remember; `if`(i*(i+1)/2 (f-> f+[0, f[1]*
       h[2]/h[1]])(b(n-i, min(n-i, i-1))*h[1]))(g(i))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..37);

Mathematica

g[n_] := g[n] = {PartitionsP[n], Sum[PartitionsP[n - j] DivisorSigma[0, j], {j, 1, n}]};
b[n_, i_] := b[n, i] = If[i(i+1)/2 < n, 0, If[n == 0, {1, 0}, Module[{h, f}, h = g[i]; f = b[n - i, Min[n - i, i - 1]] h[[1]]; b[n, i - 1] + f + {0, f[[1]] h[[2]] / h[[1]]}]]];
a[n_] := b[n, n][[2]];
a /@ Range[0, 37] (* Jean-François Alcover, Dec 05 2020, after Alois P. Heinz *)