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Sequence shifts left ten places under Weigh transform with a(n) = signum(n) for n<10.
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%I #8 May 09 2019 07:24:08

%S 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 87,114,149,195,255,334,438,574,753,989,1300,1711,2255,2973,3927,5190,

%U 6867,9092,12046,15971,21188,28124,37351,49631,65981,87763,116794

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

%H Alois P. Heinz, <a href="/A316082/b316082.txt">Table of n, a(n) for n = 0..2500</a>

%F 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 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))

%p end:

%p a:= n-> (k-> `if`(n<k, signum(n), b(n-k$2)))(10):

%p seq(a(n), n=0..55);

%Y Column k=10 of A316074.

%Y Cf. A057427, A218027.

%K nonn,eigen

%O 0,14

%A _Alois P. Heinz_, Jun 23 2018