A340508 Let ped(n) denote the number of partitions of n in which the even parts are distinct (A001935); a(n) = ped(9*n+7).

12, 132, 876, 4416, 18624, 69060, 232044, 720648, 2097612, 5781120, 15203904, 38387556, 93503052, 220586244, 505673280, 1129518564, 2464116480, 5260683840, 11010018840, 22623235620, 45700246668, 90863466372, 178000194348, 343888491684, 655760533632, 1235186054724

Offset: 0

Author

N. J. A. Sloane, Jan 26 2021

Keywords

• nonn

Comments

These are the coefficients in the left-hand side of a "surprising identity" [Hirschhorn].

References

• M. D. Hirschhorn, The Power of q, Springer, 2017. See (33.1.3) page 303.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..5000

Crossrefs

A subsequence of A001935.

Cf. A226034.

Programs

Maple

with(numtheory):
b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(
     `if`(irem(d, 4)=0, 0, d), d=divisors(j)), j=1..n)/n)
    end:
a:= n-> b(9*n+7):
seq(a(n), n=0..25);  # Alois P. Heinz, Jan 26 2021

Mathematica

b[n_] := b[n] = If[n == 0, 1, Sum[b[n - j]*Sum[
   If[Mod[d, 4] == 0, 0, d], {d, Divisors[j]}], {j, 1, n}]/n];
a[n_] := b[9n+7];
a /@ Range[0, 25] (* Jean-François Alcover, Jan 29 2021, after Alois P. Heinz *)

Formula

a(n) = 12 * A226034(n).