A161227 Number of partitions of n into Catalan numbers A000108 where every part appears at least 2 times.

0, 1, 1, 2, 1, 3, 2, 4, 3, 6, 4, 7, 6, 9, 8, 11, 10, 14, 13, 17, 16, 20, 20, 24, 24, 28, 28, 34, 33, 39, 39, 45, 45, 52, 52, 59, 59, 68, 67, 76, 76, 86, 86, 96, 97, 108, 108, 121, 121, 134, 135, 149, 150, 164, 166, 182, 183, 200, 202, 220, 222, 241, 244, 263, 267, 288, 291, 313, 317

Offset

1,4

Links

R. H. Hardin, Table of n, a(n) for n = 1..1000

Formula

G.f.: -1 + Product_{j>=1} (1 + x^(2*binomial(2j,j)/(j+1))/(1-x^(binomial(2j,j)/(j+1)))). - Emeric Deutsch, Jun 22 2009

Example

a(10)=6 because we have 55, 22222, 222211, 2221111, 22111111, and 1^(10). - Emeric Deutsch, Jun 22 2009

Maple

g := -1+product(1+x^(2*binomial(2*j, j)/(j+1))/(1-x^(binomial(2*j, j)/(j+1))), j = 1 .. 10): gser := series(g, x = 0, 75): seq(coeff(gser, x, n), n = 1 .. 70); # Emeric Deutsch, Jun 22 2009

Crossrefs

Sequence in context: A240866 A230560 A265253 * A115584 A058742 A029140

Adjacent sequences: A161224 A161225 A161226 * A161228 A161229 A161230

Keyword

nonn

Author

R. H. Hardin, Jun 06 2009

Status

approved