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%I #23 Feb 27 2022 16:11:27
%S 1,1,7,3,31,3,127,85,511,93,2047,105,8191,5461,32767,3855,131071,1533,
%T 524287,69905,299593,182361,8388607,1118481,33554431,22369621,
%U 19173961,9256395,536870911,11545611,2147483647,1431655765,8589934591
%N Reduced numerators of 2*(2^(1+n)-1)/(1+n)/(2+n).
%C a(m) is a numerator of the highest power of n coefficient in the sum of all matrix elements of n X n matrix M(i,j) = (i+j-1)^m, i,j=(1..n). E.g., a(5) = 3 because Sum_{j=1..n} Sum_{i=1..n} (i+j-1)^5 = (1/2)*(6n^7 - 5n^5 + n^3), a(6) = 127 because Sum_{j=1..n} Sum_{i=1..n} (i+j-1)^6 = (1/84)*n^2*(381n^6 - 434 n^4 + 147n^2 - 10). - _Alexander Adamchuk_, Apr 21 2006
%C a(n) is the numerator of Integral_{x=0..2} x^n*(1-abs(1-x)) dx. - _Groux Roland_, Jan 13 2011
%H J. Singh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Singh/singh8.html">On an Arithmetic Convolution</a>, J. Int. Seq. 17 (2014) # 14.6.7.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AbsoluteValue.html">Absolute Value</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnitSquareIntegral.html">Unit Square Integral</a>
%e 1, 1, 7/6, 3/2, 31/15, 3, 127/28, 85/12, 511/45, 93/5, 2047/66, ...
%t Table[(2(2^(n+1)-1))/((n+1)(n+2)),{n,0,40}]//Numerator (* _Harvey P. Dale_, Jul 14 2019 *)
%Y Cf. A116420.
%K nonn,frac
%O 0,3
%A _Eric W. Weisstein_, Feb 14 2006
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