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A316079 Sequence shifts left seven places under Weigh transform with a(n) = signum(n) for n<7.

%I A316079 #9 May 09 2019 07:00:59
%S A316079 0,1,1,1,1,1,1,1,1,1,2,2,3,4,5,6,8,11,14,19,26,35,48,65,89,122,167,
%T A316079 230,317,438,606,840,1167,1622,2260,3151,4398,6148,8601,12046,16888,
%U A316079 23697,33283,46783,65814,92654,130539,184039,259639,366533,517749,731781
%N A316079 Sequence shifts left seven places under Weigh transform with a(n) = signum(n) for n<7.
%H A316079 Alois P. Heinz, <a href="/A316079/b316079.txt">Table of n, a(n) for n = 0..2500</a>
%F A316079 G.f.: x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 * Product_{n>=1} (1 + x^n)^a(n). - _Ilya Gutkovskiy_, May 09 2019
%p A316079 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A316079       add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
%p A316079     end:
%p A316079 a:= n-> (k-> `if`(n<k, signum(n), b(n-k$2)))(7):
%p A316079 seq(a(n), n=0..51);
%Y A316079 Column k=7 of A316074.
%Y A316079 Cf. A057427, A218024.
%K A316079 nonn,eigen
%O A316079 0,11
%A A316079 _Alois P. Heinz_, Jun 23 2018