cp's OEIS Frontend

A341384 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^2.

%I A341384 #11 Feb 20 2021 05:38:10
%S A341384 1,4,14,36,89,200,434,898,1810,3548,6810,12816,23719,43250,77795,
%T A341384 138244,242920,422510,727907,1243094,2105493,3538936,5905481,9787810,
%U A341384 16118588,26383244,42936039,69491436,111884015,179239648,285775148,453550910,716670609
%N A341384 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^2.
%H A341384 Alois P. Heinz, <a href="/A341384/b341384.txt">Table of n, a(n) for n = 2..10000</a>
%F A341384 a(n) ~ A026011(n). - _Vaclav Kotesovec_, Feb 20 2021
%p A341384 g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(d^2/
%p A341384      `if`(d::odd, 1, 2), d=numtheory[divisors](j)), j=1..n)/n)
%p A341384     end:
%p A341384 b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0,
%p A341384       g(n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
%p A341384     end:
%p A341384 a:= n-> b(n, 2):
%p A341384 seq(a(n), n=2..34);  # _Alois P. Heinz_, Feb 10 2021
%t A341384 nmax = 34; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^2, {x, 0, nmax}], x] // Drop[#, 2] &
%Y A341384 Cf. A026007, A026011, A321947, A327380, A341385, A341386, A341387, A341388, A341390, A341391.
%K A341384 nonn
%O A341384 2,2
%A A341384 _Ilya Gutkovskiy_, Feb 10 2021