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A280129 Expansion of Product_{k>=2} (1 + x^(k^2)). 8
1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 2, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 3, 0, 0, 1, 1, 1, 0, 0, 1, 3, 0, 0, 2, 2, 0, 1, 2, 0, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,26
COMMENTS
Number of partitions of n into distinct squares > 1.
LINKS
FORMULA
G.f.: Product_{k>=2} (1 + x^(k^2)).
From Vaclav Kotesovec, Dec 26 2016: (Start)
a(n) = Sum_{k=0..n} (-1)^(n-k) * A033461(k).
a(n) + a(n-1) = A033461(n).
a(n) ~ A033461(n)/2.
(End)
EXAMPLE
G.f. = 1 + x^4 + x^9 + x^13 + x^16 + x^20 + 2*x^25 + 2*x^29 + x^34 + x^36 + ...
a(25) = 2 because we have [25] and [16, 9].
MATHEMATICA
nmax = 115; CoefficientList[Series[Product[1 + x^k^2, {k, 2, nmax}], {x, 0, nmax}], x]
PROG
(PARI) {a(n) = if(n < 0, 0, polcoeff( prod(k=2, sqrtint(n), 1 + x^k^2 + x*O(x^n)), n))}; /* Michael Somos, Dec 26 2016 */
CROSSREFS
Sequence in context: A263764 A325668 A070202 * A227344 A130207 A325433
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 26 2016
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)