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Expansion of e.g.f. Product_{k>=1} ((1 + x^k)/(1 - x^k))^(1/k!).
2

%I #16 Jul 01 2021 12:08:46

%S 1,2,6,26,126,742,5166,40462,351742,3458470,37425406,440788702,

%T 5633316574,77379974518,1140707915262,18053421105742,302414295475134,

%U 5364631473148614,100769601500958078,1988246969908681278,41179474537324087454,896909297854081874454

%N Expansion of e.g.f. Product_{k>=1} ((1 + x^k)/(1 - x^k))^(1/k!).

%C Exponential convolution of the sequences A209902 and A298906.

%H Seiichi Manyama, <a href="/A345870/b345870.txt">Table of n, a(n) for n = 0..449</a>

%F E.g.f.: exp( 2*Sum_{k>=0} (exp(x^(2*k+1)) - 1)/(2*k+1) ).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, ((1+x^k)/(1-x^k))^(1/k!))))

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(2*sum(k=0, N\2, (exp(x^(2*k+1))-1)/(2*k+1)))))

%Y Cf. A005408, A209902, A295792, A298906, A306041, A345871.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jun 27 2021