A216222 Counting a set of restricted partitions

1, 1, 2, 1, 1, 2, 3, 4, 3, 3, 3, 3, 6, 7, 8, 10, 9, 9, 9, 9, 11, 13, 16, 20, 22, 25, 28, 27, 28, 29, 30, 32, 35, 40, 45, 53, 60, 67, 73, 79, 85, 87, 92, 95, 98, 105, 111, 120, 132, 145, 160, 178, 196, 212, 231, 247, 263, 280, 291, 305, 319, 334, 352

Offset

0,3

Links

Table of n, a(n) for n=0..62.

Formula

G.f.: sum(k>=0, x^(k^2) * prod(j=1..k, (1+x^j)^2 ) ) = 1 +x^1*(1+x)^2 +x^4*(1+x)^2*(1+x^2)^2 +...+ x^k^2*(1+x)^2*(1+x^2)^2*(1+x^3)^2*...*(1+x^k)^2+...

Mathematica

Take[CoefficientList[Sum[x^(k^2)*Product[1 + x^i, {i, k}]^2, {k, 0, 7}], x], 63] (* Giovanni Resta, Mar 13 2013 *)

Crossrefs

Sequence in context: A208234 A092543 A277083 * A090282 A022910 A030737

Adjacent sequences: A216219 A216220 A216221 * A216223 A216224 A216225

Keyword

nonn

Author

David S. Newman, Mar 13 2013

Extensions

a(14)-a(62) from Giovanni Resta, Mar 13 2013

Status

approved