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A297193 Irregular triangle read by rows: rows are partial alternating sums of rows of A297191.

%I A297193 #11 Mar 04 2018 14:34:20
%S A297193 1,1,4,1,1,8,17,8,1,1,12,49,80,49,12,1,1,16,97,280,401,280,97,16,1,1,
%T A297193 20,161,672,1569,2084,1569,672,161,20,1,1,24,241,1320,4321,8752,11073,
%U A297193 8752,4321,1320,241,24,1,1,28,337,2288,9681,26684,48833,59712,48833,26684,9681
%N A297193 Irregular triangle read by rows: rows are partial alternating sums of rows of A297191.
%H A297193 I. Sugai, <a href="/A007401/a007401_7.pdf">Numerical solutions of Laplace's Equation, given Cauchy conditions</a>, IBM Journal 3 (1959), 187-188. (Annotated scanned copy.) A signed version of the triangle appears on page 188, but the signs are not important.
%e A297193 Triangle begins:
%e A297193 1,
%e A297193 1,4,1,
%e A297193 1,8,17,8,1,
%e A297193 1,12,49,80,49,12,1,
%e A297193 1,16,97,280,401,280,97,16,1,
%e A297193 1,20,161,672,1569,2084,1569,672,161,20,1,
%e A297193 ...
%p A297193 A297191x := proc(n,k)
%p A297193     A008288(2*n+1,k) ;
%p A297193 end proc:
%p A297193 A297193 := proc(n,k)
%p A297193     add((-1)^(i+1)*A297191x(n,i),i=0..k) ;
%p A297193     abs(%) ;
%p A297193 end proc:
%p A297193 seq(seq(A297193(n,k),k=0..2*n),n=0..10) ; # _R. J. Mathar_, Mar 04 2018
%Y A297193 Cf. A008288, A297191, A297194.
%Y A297193 The middle and next to middle columns are A089165 and A089383.
%K A297193 nonn,tabf
%O A297193 0,3
%A A297193 _N. J. A. Sloane_, Jan 10 2018