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%I #28 Aug 02 2018 15:44:12
%S 1,6,18,46,107,241,535,1178,2569,5546,11859,25156,53058,111379,232966,
%T 486023,1012185,2104729,4370644,9064924,18778766,38856079,80307630,
%U 165790125,341872016,704171185,1448812630,2977673003,6113469501,12538958895,25693167881,52598980642
%N a(n) = Sum_{k=0..2^n-1} k*A261015(n,k).
%C The scaled values a(n)/2^n are (to nine decimal places) 0.5000000000, 1.500000000, 2.250000000, 2.875000000, 3.343750000, 3.765625000, 4.179687500, 4.601562500, 5.017578125, 5.416015625, 5.790527344, 6.141601562, 6.476806641, 6.798034668, 7.109558105, 7.416122437, 7.722358704, 8.028903961, 8.336341858, 8.644985199, 8.954413414, 9.264011145, 9.573415518, 9.881861508, 10.18858004, 10.49296834, 10.79449527, 11.09269635, 11.38722431, 11.67781548, 11.96431363, 12.24665452, ...
%H Alois P. Heinz and Hiroaki Yamanouchi, <a href="/A261016/b261016.txt">Table of n, a(n) for n = 1..58</a> (a(1)-a(36) from Alois P. Heinz)
%t (* This program is not suitable to compute more than a dozen terms. *)
%t notVis[bits_] := For[i = 0, True, i++, If[SequencePosition[bits, IntegerDigits[i, 2]] == {}, Return[i]]];
%t T[n_, k_] := Select[Rest[IntegerDigits[#, 2]] & /@ Range[2^n, 2^(n+1) - 1], notVis[#] == k &] // Length;
%t a[n_] := Sum[k*T[n, k], {k, 0, 2^n - 1}];
%t Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 12}] (* _Jean-François Alcover_, Aug 02 2018 *)
%o (Haskell)
%o a261016 = sum . zipWith (*) [0..] . a261019_row'
%o -- _Reinhard Zumkeller_, Aug 18 2015
%Y Cf. A261019, A261015, A260273.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Aug 16 2015
%E a(5)-a(16) from _Alois P. Heinz_, Aug 17 2015
%E a(17)-a(25) from _Reinhard Zumkeller_, Aug 18 2015
%E a(26)-a(32) from _Alois P. Heinz_, Aug 19 2015
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