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A316077 Sequence shifts left five places under Weigh transform with a(n) = signum(n) for n<5.

%I A316077 #10 May 09 2019 07:00:27
%S A316077 0,1,1,1,1,1,1,1,2,2,3,4,5,7,10,14,20,28,40,58,84,121,176,257,376,552,
%T A316077 812,1196,1767,2615,3877,5757,8562,12751,19018,28400,42461,63554,
%U A316077 95234,142845,214473,322310,484793,729797,1099509,1657761,2501299,3776681
%N A316077 Sequence shifts left five places under Weigh transform with a(n) = signum(n) for n<5.
%H A316077 Alois P. Heinz, <a href="/A316077/b316077.txt">Table of n, a(n) for n = 0..2000</a>
%F A316077 G.f.: x + x^2 + x^3 + x^4 + x^5 * Product_{n>=1} (1 + x^n)^a(n). - _Ilya Gutkovskiy_, May 09 2019
%p A316077 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A316077       add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
%p A316077     end:
%p A316077 a:= n-> (k-> `if`(n<k, signum(n), b(n-k$2)))(5):
%p A316077 seq(a(n), n=0..47);
%Y A316077 Column k=5 of A316074.
%Y A316077 Cf. A057427, A218022.
%K A316077 nonn,eigen
%O A316077 0,9
%A A316077 _Alois P. Heinz_, Jun 23 2018