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A283984 Sums of distinct nonzero terms of A007489: a(n) = Sum_{k>=0} A030308(n,k)*A007489(1+k).

%I A283984 #14 Mar 19 2017 19:40:03
%S A283984 0,1,3,4,9,10,12,13,33,34,36,37,42,43,45,46,153,154,156,157,162,163,
%T A283984 165,166,186,187,189,190,195,196,198,199,873,874,876,877,882,883,885,
%U A283984 886,906,907,909,910,915,916,918,919,1026,1027,1029,1030,1035,1036,1038,1039,1059,1060,1062,1063,1068,1069,1071,1072,5913
%N A283984 Sums of distinct nonzero terms of A007489: a(n) = Sum_{k>=0} A030308(n,k)*A007489(1+k).
%C A283984 Indexing starts from zero, with a(0) = 0.
%H A283984 Antti Karttunen, <a href="/A283984/b283984.txt">Table of n, a(n) for n = 0..8191</a>
%H A283984 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A283984 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A283984 a(n) = Sum_{i=0..A070939(n)} A030308(n,i)*A007489(1+i).
%F A283984 a(n) = A276075(A283477(n)).
%F A283984 Other identities. For all n >= 0:
%F A283984 a(2^n) = A007489(n+1).
%o A283984 (PARI)
%o A283984 A007489(n) = sum(k=1, n, k!);
%o A283984 A030308(n,k) = bittest(n,k);
%o A283984 A283984(n) = sum(i=0,(#binary(n)-1),A030308(n,i)*A007489(1+i));
%o A283984 (Scheme) (define (A283984 n) (A276075 (A283477 n)))
%Y A283984 Cf. A000142, A007489, A030308, A059590, A070939, A276075, A276091, A283477, A283985.
%K A283984 nonn
%O A283984 0,3
%A A283984 _Antti Karttunen_, Mar 19 2017