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A316082 Sequence shifts left ten places under Weigh transform with a(n) = signum(n) for n<10.

%I A316082 #8 May 09 2019 07:24:08
%S A316082 0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,4,5,6,8,10,12,15,19,24,31,40,51,67,
%T A316082 87,114,149,195,255,334,438,574,753,989,1300,1711,2255,2973,3927,5190,
%U A316082 6867,9092,12046,15971,21188,28124,37351,49631,65981,87763,116794
%N A316082 Sequence shifts left ten places under Weigh transform with a(n) = signum(n) for n<10.
%H A316082 Alois P. Heinz, <a href="/A316082/b316082.txt">Table of n, a(n) for n = 0..2500</a>
%F A316082 G.f.: x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 * Product_{n>=1} (1 + x^n)^a(n). - _Ilya Gutkovskiy_, May 09 2019
%p A316082 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A316082       add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
%p A316082     end:
%p A316082 a:= n-> (k-> `if`(n<k, signum(n), b(n-k$2)))(10):
%p A316082 seq(a(n), n=0..55);
%Y A316082 Column k=10 of A316074.
%Y A316082 Cf. A057427, A218027.
%K A316082 nonn,eigen
%O A316082 0,14
%A A316082 _Alois P. Heinz_, Jun 23 2018