A116419 Reduced numerators of 2*(2^(1+n)-1)/(1+n)/(2+n).

1, 1, 7, 3, 31, 3, 127, 85, 511, 93, 2047, 105, 8191, 5461, 32767, 3855, 131071, 1533, 524287, 69905, 299593, 182361, 8388607, 1118481, 33554431, 22369621, 19173961, 9256395, 536870911, 11545611, 2147483647, 1431655765, 8589934591

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

Table of n, a(n) for n=0..32.

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

Cf. A116420.

Sequence in context: A213561 A368350 A253892 * A290235 A225825 A199927

Adjacent sequences: A116416 A116417 A116418 * A116420 A116421 A116422

Keyword

nonn,frac

Author

Eric W. Weisstein, Feb 14 2006

Status

approved