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%I #14 Nov 03 2017 11:00:09
%S 1,1,1,1,-1,3,-5,7,-7,3,5,-9,-17,129,-417,977,-1809,2591,-2317,-1061,
%T 10485,-27983,49165,-51319,-26861,311455,-1011473,2393275,-4643591,
%U 7521265,-9694135,7738137,4976985,-38789975,106112817,-215068927,354515933,-464539803
%N Inverse binomial transform of the number of overpartitions (A015128).
%H Vaclav Kotesovec, <a href="/A294499/b294499.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A015128(k).
%F a(n) = [x^n] (1 - x)^n/theta_4(x), where theta_4() is the Jacobi theta function. - _Ilya Gutkovskiy_, Nov 03 2017
%t Table[Sum[(-1)^(n-k)*Binomial[n, k]*Sum[PartitionsP[k-j]*PartitionsQ[j], {j, 0, k}], {k, 0, n}], {n, 0, 50}]
%Y Cf. A266497, A281425, A293467.
%K sign
%O 0,6
%A _Vaclav Kotesovec_, Nov 01 2017
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