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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.
1
-1, -3, 0, -7, -4, 2, -15, -18, -2, 5, -31, -64, -28, 5, 9, -63, -210, -158, -25, 19, 14, -127, -664, -748, -271, 9, 42, 20, -255, -2058, -3302, -1825, -317, 98, 76, 27, -511, -6304, -14068, -10735, -3351, -126, 272, 123, 35, -1023, -19170, -58718, -59425, -26141, -4606, 580, 567, 185, 44
OFFSET
1,2
COMMENTS
Paul Erdős conjectured that A(n, k) = 0 only for (n, k) = (2, 1).
EXAMPLE
Array starts
-1, -3, -7, -15, -31, -63, -127, -255
0, -4, -18, -64, -210, -664, -2058, -6304
2, -2, -28, -158, -748, -3302, -14068, -58718
5, 5, -25, -271, -1825, -10735, -59425, -318271
9, 19, 9, -317, -3351, -26141, -183111, -1216637
14, 42, 98, -126, -4606, -50478, -446782, -3622206
20, 76, 272, 580, -3760, -77324, -896848, -8869820
27, 123, 567, 2211, 2727, -84477, -1485513, -18362109
35, 185, 1025, 5333, 20825, -21595, -1919575, -32268667
44, 264, 1694, 10692, 59774, 206844, -1406746, -46627548
PROG
(PARI) x(n, k) = sum(i=1, n, i^k)
y(n, k) = (n+1)^k
a(n, k) = x(n, k) - y(n, k)
array(rows, cols) = for(s=1, rows, for(t=1, cols, print1(a(s, t), ", ")); print(""))
array(10, 8) \\ print initial 10 rows and 8 columns of array
CROSSREFS
Cf. A000096 (column 1), A126646 (row 1), A191686 (main diagonal).
Sequence in context: A363392 A098867 A062253 * A369094 A322018 A200339
KEYWORD
sign,tabl
AUTHOR
Felix Fröhlich, Aug 12 2017
STATUS
approved