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A316081 Sequence shifts left nine places under Weigh transform with a(n) = signum(n) for n<9.

%I A316081 #11 May 09 2019 07:24:20
%S A316081 0,1,1,1,1,1,1,1,1,1,1,1,2,2,3,4,5,6,8,10,12,16,20,26,35,45,59,79,104,
%T A316081 137,183,242,320,427,567,754,1008,1345,1797,2409,3228,4328,5817,7817,
%U A316081 10511,14154,19063,25689,34655,46768,63148,85336,115372,156057,211233
%N A316081 Sequence shifts left nine places under Weigh transform with a(n) = signum(n) for n<9.
%H A316081 Alois P. Heinz, <a href="/A316081/b316081.txt">Table of n, a(n) for n = 0..2500</a>
%F A316081 G.f.: x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 * Product_{n>=1} (1 + x^n)^a(n). - _Ilya Gutkovskiy_, May 09 2019
%p A316081 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A316081       add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
%p A316081     end:
%p A316081 a:= n-> (k-> `if`(n<k, signum(n), b(n-k$2)))(9):
%p A316081 seq(a(n), n=0..54);
%Y A316081 Column k=9 of A316074.
%Y A316081 Cf. A057427, A218026.
%K A316081 nonn,eigen
%O A316081 0,13
%A A316081 _Alois P. Heinz_, Jun 23 2018