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Triangle of Stirling numbers of second kind (A048993) read mod 2.
1

%I #18 Aug 09 2017 06:19:58

%S 1,0,1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,1,1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,0,

%T 1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,1,0,1,

%U 1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,1

%N Triangle of Stirling numbers of second kind (A048993) read mod 2.

%C Also parity of triangles A103631, A121314, A133607, A208345. - _Philippe Deléham_, Jun 04 2012

%D Brand, Neal; Das, Sajal; Jacob, Tom. The number of nonzero entries in recursively defined tables modulo primes. Proceedings of the Twenty-first Southeastern Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1990). Congr. Numer. 78 (1990), 47--59. MR1140469 (92h:05004).

%H Bill Gosper, <a href="/A008277/a008277.png">Colored illustrations of triangle of Stirling numbers of second kind read mod 2, 3, 4, 5, 6, 7</a>

%e Triangle starts:

%e 1;

%e 0, 1;

%e 0, 1, 1;

%e 0, 1, 1, 1;

%e 0, 1, 1, 0, 1;

%e 0, 1, 1, 1, 0, 1;

%e ...

%t Table[Mod[StirlingS2[n, k], 2], {n, 0, 13}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Apr 03 2016 *)

%o (PARI) for(n=0, 22, for(k=0, n, print1(stirling(n, k, 2) % 2, ", ")); print()); \\ _Michel Marcus_, Apr 03 2016

%Y Cf. A008277, A048993, A087748.

%K nonn,tabl

%O 0

%A _N. J. A. Sloane_, Jun 03 2012