%I #17 Oct 02 2023 13:15:22
%S 1,3,2,7,4,2,9,2,-2,-4,13,4,2,4,8,15,2,-2,-4,-8,-16,21,6,4,6,10,18,34,
%T 25,4,-2,-6,-12,-22,-40,-74,31,6,2,4,10,22,44,84,158,33,2,-4,-6,-10,
%U -20,-42,-86,-170,-328,37,4,2,6,12,22,42,84,170,340,668
%N Iterated differences of lucky numbers. Array read by antidiagonals, n >= 0, k >= 1: T(0,k) = A000959(k), T(n,k) = T(n-1,k+1) - T(n-1,k) for n > 0.
%H Winston de Greef, <a href="/A350001/b350001.txt">Table of n, a(n) for n = 0..11324</a> (150 antidiagonals)
%H <a href="/index/Lu#lucky_numbers">Index entries for sequences related to lucky numbers</a>
%F T(n,k) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*A000959(k+j).
%e Array begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12
%e ---+--------------------------------------------------------------
%e 0 | 1 3 7 9 13 15 21 25 31 33 37 43
%e 1 | 2 4 2 4 2 6 4 6 2 4 6 6
%e 2 | 2 -2 2 -2 4 -2 2 -4 2 2 0 -4
%e 3 | -4 4 -4 6 -6 4 -6 6 0 -2 -4 14
%e 4 | 8 -8 10 -12 10 -10 12 -6 -2 -2 18 -32
%e 5 | -16 18 -22 22 -20 22 -18 4 0 20 -50 56
%e 6 | 34 -40 44 -42 42 -40 22 -4 20 -70 106 -82
%e 7 | -74 84 -86 84 -82 62 -26 24 -90 176 -188 102
%e 8 | 158 -170 170 -166 144 -88 50 -114 266 -364 290 -100
%e 9 | -328 340 -336 310 -232 138 -164 380 -630 654 -390 50
%e 10 | 668 -676 646 -542 370 -302 544 -1010 1284 -1044 440 78
%Y Cf. A000959 (row n = 0), A031883 (row n = 1), A123593 (column k = 1).
%Y Cf. A254967 (absolute differences), A095195 (iterated differences of primes), A350004 (iterated differences of ludic numbers).
%K sign,tabl
%O 0,2
%A _Pontus von Brömssen_, Dec 08 2021