# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a294582 Showing 1-1 of 1 %I A294582 #16 Nov 04 2017 08:11:06 %S A294582 1,1,1,1,1,3,1,1,5,6,1,1,9,14,13,1,1,17,36,42,24,1,1,33,98,148,103,48, %T A294582 1,1,65,276,546,489,289,86,1,1,129,794,2068,2467,1959,690,160,1,1,257, %U A294582 2316,7962,12969,14281,6326,1771,282,1,1,513,6818,30988,70243 %N A294582 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1 - j^k*x^j)^j. %H A294582 Seiichi Manyama, Antidiagonals n = 0..139, flattened %F A294582 A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(2+k*j/d)) * A(n-j,k) for n > 0. %e A294582 Square array begins: %e A294582 1, 1, 1, 1, 1, ... %e A294582 1, 1, 1, 1, 1, ... %e A294582 3, 5, 9, 17, 33, ... %e A294582 6, 14, 36, 98, 276, ... %e A294582 13, 42, 148, 546, 2068, ... %Y A294582 Columns k=0..2 give A000219, A266941, A285674. %Y A294582 Rows n=0-1 give A000012. %Y A294582 Cf. A292193, A294580. %K A294582 nonn,tabl %O A294582 0,6 %A A294582 _Seiichi Manyama_, Nov 02 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE