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A290844 Square array read by antidiagonals downwards: A(n, k) = (Sum_{i=1..n} i^k) - (n+1)^k for n >= 1, k >= 1.

%I A290844 #17 Sep 03 2017 22:06:58
%S A290844 -1,-3,0,-7,-4,2,-15,-18,-2,5,-31,-64,-28,5,9,-63,-210,-158,-25,19,14,
%T A290844 -127,-664,-748,-271,9,42,20,-255,-2058,-3302,-1825,-317,98,76,27,
%U A290844 -511,-6304,-14068,-10735,-3351,-126,272,123,35,-1023,-19170,-58718,-59425,-26141,-4606,580,567,185,44
%N A290844 Square array read by antidiagonals downwards: A(n, k) = (Sum_{i=1..n} i^k) - (n+1)^k for n >= 1, k >= 1.
%C A290844 Paul Erdős conjectured that A(n, k) = 0 only for (n, k) = (2, 1).
%H A290844 Wikipedia, <a href="https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Moser_equation">Erdos-Moser equation</a>
%e A290844 Array starts
%e A290844   -1,  -3,   -7,   -15,   -31,    -63,     -127,      -255
%e A290844    0,  -4,  -18,   -64,  -210,   -664,    -2058,     -6304
%e A290844    2,  -2,  -28,  -158,  -748,  -3302,   -14068,    -58718
%e A290844    5,   5,  -25,  -271, -1825, -10735,   -59425,   -318271
%e A290844    9,  19,    9,  -317, -3351, -26141,  -183111,  -1216637
%e A290844   14,  42,   98,  -126, -4606, -50478,  -446782,  -3622206
%e A290844   20,  76,  272,   580, -3760, -77324,  -896848,  -8869820
%e A290844   27, 123,  567,  2211,  2727, -84477, -1485513, -18362109
%e A290844   35, 185, 1025,  5333, 20825, -21595, -1919575, -32268667
%e A290844   44, 264, 1694, 10692, 59774, 206844, -1406746, -46627548
%o A290844 (PARI) x(n, k) = sum(i=1, n, i^k)
%o A290844 y(n, k) = (n+1)^k
%o A290844 a(n, k) = x(n, k) - y(n, k)
%o A290844 array(rows, cols) = for(s=1, rows, for(t=1, cols, print1(a(s, t), ", ")); print(""))
%o A290844 array(10, 8) \\ print initial 10 rows and 8 columns of array
%Y A290844 Cf. A000096 (column 1), A126646 (row 1), A191686 (main diagonal).
%K A290844 sign,tabl
%O A290844 1,2
%A A290844 _Felix Fröhlich_, Aug 12 2017