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%I #9 May 29 2018 08:22:00
%S 0,1,1,1,2,2,3,3,4,5,6,7,8,10,11,13,15,18,20,23,26,30,34,38,43,49,55,
%T 61,69,77,86,95,106,118,131,144,160,177,195,214,236,260,285,312,342,
%U 375,410,447,488,534,581,632,688,749,813,882,957,1039,1125,1217,1317,1426
%N Number of partitions of n into distinct parts with exactly one even part.
%F G.f.: x^2/(1-x^2)*Product(1+x^(2*i+1), i=0..infinity). More generally, g.f. for number of partitions of n into distinct parts with exactly k even parts is x^(k*(k+1))/Product(1-x^(2*i), i=1..k)*Product(1+x^(2*i+1), i=0..infinity).
%F a(n) ~ 3^(1/4) * exp(Pi*sqrt(n/6)) / (2^(5/4) * Pi * n^(1/4)). - _Vaclav Kotesovec_, May 29 2018
%t Drop[ CoefficientList[ Series[x^2/(1 - x^2) * Product[1 + x^(2*i + 1), {i, 0, 70}], {x, 0, 62}], x], 1] (* _Robert G. Wilson v_, Aug 21 2004 *)
%Y Cf. A000700.
%K easy,nonn
%O 1,5
%A _Vladeta Jovovic_, Aug 17 2004
%E More terms from _Robert G. Wilson v_, Aug 21 2004