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%I #26 Feb 01 2017 13:12:04
%S 2,3,1,5,2,1,7,2,0,-1,11,4,2,2,3,13,2,-2,-4,-6,-9,17,4,2,4,8,14,23,19,
%T 2,-2,-4,-8,-16,-30,-53,23,4,2,4,8,16,32,62,115,29,6,2,0,-4,-12,-28,
%U -60,-122,-237,31,2,-4,-6,-6,-2,10,38,98,220,457,37,6,4,8,14,20,22,12
%N T(n,0) = prime(n), T(n,k) = T(n,k-1)-T(n-1,k-1), 0<=k<n, triangle read by rows.
%C T(n,0)=A000040(n); T(n,1)=A001223(n-1) for n>1; T(n,2)=A036263(n-2) for n>2; T(n,n-1)=A007442(n) for n>1.
%H Alois P. Heinz, <a href="/A095195/b095195.txt">Rows n = 1..141, flattened</a>
%e Triangle begins:
%e 2;
%e 3, 1;
%e 5, 2, 1;
%e 7, 2, 0, -1;
%e 11, 4, 2, 2, 3;
%e 13, 2, -2, -4, -6, -9;
%e Alternative: array form read by antidiagonals:
%e 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,...
%e 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6,...
%e 1, 0, 2, -2, 2, -2, 2, 2, -4, 4, -2,...
%e -1, 2, -4, 4, -4, 4, 0, -6, 8, -6, 0,...
%e 3, -6, 8, -8, 8, -4, -6, 14, -14, 6, 4,...
%e -9, 14, -16, 16, -12, -2, 20, -28, 20, -2, -8,...
%e 23, -30, 32, -28, 10, 22, -48, 48, -22, -6, 10,..,
%e -53, 62, -60, 38, 12, -70, 96, -70, 16, 16, -12,...
%e 115,-122, 98, -26, -82, 166,-166, 86, 0, -28, 28,...
%e -237, 220,-124, -56, 248,-332, 252, -86, -28, 56, -98,...
%e 457,-344, 68, 304,-580, 584,-338, 58, 84,-154, 308,...
%p A095195A := proc(n,k) # array, k>=0, n>=0
%p option remember;
%p if n =0 then
%p ithprime(k+1) ;
%p else
%p procname(n-1,k+1)-procname(n-1,k) ;
%p end if;
%p end proc:
%p A095195 := proc(n,k) # triangle, 0<=k<n, n>=1
%p A095195A(k,n-k-1) ;
%p end proc: # _R. J. Mathar_, Sep 19 2013
%t T[n_, 0] := Prime[n]; T[n_, k_] /; 0 <= k < n := T[n, k] = T[n, k-1] - T[n-1, k-1]; Table[T[n, k], {n, 1, 12}, {k, 0, n-1}] // Flatten (* _Jean-François Alcover_, Feb 01 2017 *)
%o (Haskell)
%o a095195 n k = a095195_tabl !! (n-1) !! (k-1)
%o a095195_row n = a095195_tabl !! (n-1)
%o a095195_tabl = f a000040_list [] where
%o f (p:ps) xs = ys : f ps ys where ys = scanl (-) p xs
%o -- _Reinhard Zumkeller_, Oct 10 2013
%Y Cf. A036262-A036271.
%Y Cf. A140119 (row sums).
%K sign,tabl,look
%O 1,1
%A _Reinhard Zumkeller_, Jun 22 2004
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