OFFSET
0,3
COMMENTS
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
a(n) is the numerator of Integral_{x=0..2} x^n*(1-abs(1-x)) dx. - Groux Roland, Jan 13 2011
LINKS
J. Singh, On an Arithmetic Convolution, J. Int. Seq. 17 (2014) # 14.6.7.
Eric Weisstein's World of Mathematics, Absolute Value
Eric Weisstein's World of Mathematics, Unit Square Integral
EXAMPLE
1, 1, 7/6, 3/2, 31/15, 3, 127/28, 85/12, 511/45, 93/5, 2047/66, ...
MATHEMATICA
Table[(2(2^(n+1)-1))/((n+1)(n+2)), {n, 0, 40}]//Numerator (* Harvey P. Dale, Jul 14 2019 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, Feb 14 2006
STATUS
approved