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G.f.: g(x) * g(x^2), where g(x) is the g.f. of A000081.
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%I #7 Dec 26 2020 02:48:19

%S 0,0,0,1,1,3,5,13,26,65,147,369,899,2298,5851,15261,39945,105948,

%T 282504,759480,2052027,5576017,15216998,41705762,114715503,316611401,

%U 876466003,2433091773,6771462322,18889829555,52809592990,147935027381,415182991401,1167251435240

%N G.f.: g(x) * g(x^2), where g(x) is the g.f. of A000081.

%H Vaclav Kotesovec, <a href="/A339984/b339984.txt">Table of n, a(n) for n = 0..2000</a>

%F a(n) ~ A339986 * A051491^n / n^(3/2).

%t max = 30; A000081 = Rest[Cases[ Import["https://oeis.org/A000081/b000081.txt", "Table"], {_, _}][[All, 2]]]; g81 = Sum[A000081[[k]]*x^k, {k, 1, max}]; g81x2 = Sum[A000081[[k]]*x^(2*k), {k, 1, max}]; CoefficientList[Series[g81 * g81x2, {x, 0, max}], x]

%Y Cf. A000081, A217781, A309619, A339985.

%K nonn

%O 0,6

%A _Vaclav Kotesovec_, Dec 25 2020