A052337 Number of partitions into at most a(1) copies of 1, a(2) copies of 2, ...

1, 1, 1, 2, 2, 3, 5, 6, 8, 10, 13, 17, 21, 27, 34, 42, 53, 65, 80, 98, 119, 146, 177, 213, 258, 309, 370, 443, 528, 628, 746, 883, 1044, 1231, 1449, 1703, 1997, 2338, 2734, 3190, 3718, 4325, 5025, 5830, 6754, 7816, 9032, 10422, 12016, 13832, 15907, 18274

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

E.g.f. satisfies A(x) = Product_{i>=1} (1-x^(a(i)*(i+1)))/(1-x^i).

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(b(n-i*j, i-1), j=0..min(n/i, a(i)))))
    end:
a:= n-> `if`(n=0, 0, 1)+b(n, n-1):
seq(a(n), n=0..70);  # Alois P. Heinz, Jun 12 2018

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i j, i - 1], {j, 0, Min[n/i, a[i]]}]]];
a[n_] := If[n == 0, 0, 1] + b[n, n - 1];
a /@ Range[0, 70] (* Jean-François Alcover, Nov 23 2020, after Alois P. Heinz *)

Crossrefs

Cf. A289501.

Sequence in context: A035631 A050046 A387178 * A308858 A192432 A121081

Adjacent sequences: A052334 A052335 A052336 * A052338 A052339 A052340

Keyword

nonn,eigen

Author

Christian G. Bower, Dec 19 1999

Status

approved