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Binomial transform of A015128.
7

%I #10 Apr 20 2018 17:51:43

%S 1,3,9,27,79,225,627,1717,4633,12341,32501,84737,218959,561263,

%T 1428287,3610671,9072367,22668285,56345835,139382713,343242533,

%U 841713531,2055944117,5003148987,12132552115,29323810757,70651867863,169719163521,406541986857,971192810019

%N Binomial transform of A015128.

%H Vaclav Kotesovec, <a href="/A266497/b266497.txt">Table of n, a(n) for n = 0..3000</a>

%F a(n) ~ 2^(n-2) * exp(Pi*sqrt(n/2) + Pi^2/16) / n.

%F a(n) = [x^n] (1 + x)^n/theta_4(x), where theta_4() is the Jacobi theta function. - _Ilya Gutkovskiy_, Apr 20 2018

%t A015128[n_]:=Sum[PartitionsP[n-k]*PartitionsQ[k], {k, 0, n}];

%t Table[Sum[Binomial[n, k]*A015128[k], {k, 0, n}], {n, 0, 30}]

%Y Cf. A015128, A218481, A266232, A294499.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Dec 30 2015