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A316080 Sequence shifts left eight places under Weigh transform with a(n) = signum(n) for n<8.

%I A316080 #10 May 09 2019 07:01:12
%S A316080 0,1,1,1,1,1,1,1,1,1,1,2,2,3,4,5,6,8,10,13,17,22,30,40,53,71,96,128,
%T A316080 173,233,314,425,575,780,1060,1442,1964,2680,3658,5000,6840,9366,
%U A316080 12835,17604,24164,33194,45632,62775,86417,119038,164077,226287,312261,431138
%N A316080 Sequence shifts left eight places under Weigh transform with a(n) = signum(n) for n<8.
%H A316080 Alois P. Heinz, <a href="/A316080/b316080.txt">Table of n, a(n) for n = 0..2500</a>
%F A316080 G.f.: x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 * Product_{n>=1} (1 + x^n)^a(n). - _Ilya Gutkovskiy_, May 09 2019
%p A316080 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A316080       add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
%p A316080     end:
%p A316080 a:= n-> (k-> `if`(n<k, signum(n), b(n-k$2)))(8):
%p A316080 seq(a(n), n=0..53);
%Y A316080 Column k=8 of A316074.
%Y A316080 Cf. A057427, A218025.
%K A316080 nonn,eigen
%O A316080 0,12
%A A316080 _Alois P. Heinz_, Jun 23 2018