A327554 Number of partitions in all twice partitions of n where the second partition is strict.

0, 1, 3, 7, 15, 29, 60, 108, 201, 364, 643, 1106, 1944, 3253, 5493, 9183, 15161, 24727, 40559, 65173, 104963, 167747, 266452, 420329, 663658, 1036765, 1618221, 2514169, 3891121, 5992868, 9224213, 14107699, 21548428, 32798065, 49779331, 75301296, 113757367

Offset: 0

Author

Alois P. Heinz, Sep 16 2019

Keywords

• nonn

Examples

			a(3) = 7 = 1+1+2+3 counting the partitions in 3, 21, 2|1, 1|1|1.
		

Links

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

Crossrefs

Cf. A000009, A000041, A270995, A327608.

Programs

Maple

g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(
     `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
    end:
b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
      b(n, i-1) +(p-> p+[0, p[1]])(g(i)*b(n-i, min(n-i, i)))))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..42);

Mathematica

g[n_] := g[n] = If[n == 0, 1, Sum[g[n - j] Sum[If[OddQ[d], d, 0], {d, Divisors[j]}], {j, 1, n}]/n];
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]]}][g[i] b[n - i, Min[n - i, i]]]]];
a[n_] := b[n, n][[2]];
a /@ Range[0, 42] (* Jean-François Alcover, Dec 18 2020, after Alois P. Heinz *)