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A341390 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^7.

%I A341390 #9 Feb 10 2021 18:33:49
%S A341390 1,14,119,756,3969,18102,74102,278161,972447,3202521,10022705,
%T A341390 30013914,86475340,240787680,650356936,1709167922,4381936874,
%U A341390 10984062425,26971690900,64986689201,153866265007,358443604177,822523519244,1861072144260,4155817046514
%N A341390 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^7.
%H A341390 Alois P. Heinz, <a href="/A341390/b341390.txt">Table of n, a(n) for n = 7..10000</a>
%p A341390 g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(d^2/
%p A341390      `if`(d::odd, 1, 2), d=numtheory[divisors](j)), j=1..n)/n)
%p A341390     end:
%p A341390 b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0,
%p A341390       g(n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
%p A341390     end:
%p A341390 a:= n-> b(n, 7):
%p A341390 seq(a(n), n=7..31);  # _Alois P. Heinz_, Feb 10 2021
%t A341390 nmax = 31; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &
%Y A341390 Cf. A026007, A321952, A327385, A341384, A341385, A341386, A341387, A341388, A341391.
%K A341390 nonn
%O A341390 7,2
%A A341390 _Ilya Gutkovskiy_, Feb 10 2021