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%I #11 Nov 20 2014 15:08:15
%S 1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0,
%T 0,1,0,0,0,0,1,0,0,0,1,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,
%U 0,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,1,1,1,1,1,1,1
%N Triangle read by rows: Stirling numbers of the first kind (A008275) mod 2.
%C Essentially also parity of Mitrinovic's triangles A049458, A049460, A051339, A051380.
%D Das, Sajal K., Joydeep Ghosh, and Narsingh Deo. "Stirling networks: a versatile combinatorial topology for multiprocessor systems." Discrete applied mathematics 37 (1992): 119-146. See p. 122. - _N. J. A. Sloane_, Nov 20 2014
%F T(n, k) = A087748(n, k) = A008275(n, k) mod 2 = A047999([n/2], k-[(n+1)/ 2]) = T(n-2, k-2) XOR T(n-2, k-1) with T(1, 1) = T(2, 1) = T(2, 2) = 1; T(2n, k) = T(2n-1, k-1) XOR T(2n-1, k); T(2n+1, k) = T(2n, k-1). - _Henry Bottomley_, Dec 01 2003
%e Triangle begins:
%e 1
%e 1 1
%e 0 1 1
%e 0 1 0 1
%e 0 0 1 0 1
%e 0 0 1 1 1 1
%e 0 0 0 1 1 1 1
%e 0 0 0 1 0 0 0 1
%e 0 0 0 0 1 0 0 0 1
%e 0 0 0 0 1 1 0 0 1 1
%e 0 0 0 0 0 1 1 0 0 1 1
%e 0 0 0 0 0 1 0 1 0 1 0 1
%e 0 0 0 0 0 0 1 0 1 0 1 0 1
%e 0 0 0 0 0 0 1 1 1 1 1 1 1 1
%o (PARI) p = 2; s=14; S1T = matrix(s,s,n,k, if(k==1,(-1)^(n-1)*(n-1)!)); for(n=2,s,for(k=2,n, S1T[n,k]=-(n-1)*S1T[n-1,k]+S1T[n-1,k-1]));
%o S1TMP = matrix(s,s,n,k, S1T[n,k]%p);
%o for(n=1,s,for(k=1,n,print1(S1TMP[n,k]," "));print()) /* _Gerald McGarvey_, Oct 17 2009 */
%K easy,nonn,tabl
%O 1,1
%A _Philippe Deléham_, Oct 02 2003
%E Edited and extended by _Henry Bottomley_, Dec 01 2003
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