A032303 "EFK" (unordered, size, unlabeled) transform of 2,1,1,1,...

1, 2, 1, 3, 3, 4, 6, 7, 9, 11, 15, 17, 22, 26, 32, 39, 47, 55, 67, 79, 93, 111, 130, 152, 178, 208, 241, 281, 325, 375, 433, 499, 571, 657, 751, 858, 980, 1116, 1268, 1442, 1635, 1851, 2095, 2367, 2669, 3011, 3389, 3809, 4281, 4803, 5383, 6030, 6746, 7538

Offset: 0

Author

Christian G. Bower

Keywords

• nonn

Comments

Number of partitions of n into distinct parts with two kinds of one. - Andrew Howroyd, Jun 21 2018

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• C. G. Bower, Transforms (2)

Crossrefs

Cf. A032006.

Programs

PARI

{my(n=60); Vec((1+2*x)*prod(k=2, n, 1+x^k + O(x*x^n)))} \\ Andrew Howroyd, Jun 21 2018

Formula

G.f.: (1+2*x) * Product_{k=2..infinity} (1+x^k).

Extensions

a(0)=1 prepended and terms a(50) and beyond from Andrew Howroyd, Jun 21 2018