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A216222 Counting a set of restricted partitions 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 25 12:30 EDT 2019. Contains 323568 sequences. (Running on oeis4.)