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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 Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 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 Cf. A001156, A033461, A078134. Sequence in context: A263764 A325668 A070202 * A227344 A130207 A325433 Adjacent sequences:  A280126 A280127 A280128 * A280130 A280131 A280132 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Dec 26 2016 STATUS approved

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Last modified August 10 00:32 EDT 2022. Contains 356026 sequences. (Running on oeis4.)