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 A180957 Generalized Narayana triangle for (-1)^n. 1

%I

%S 1,1,1,1,1,1,1,0,0,1,1,-2,-5,-2,1,1,-5,-15,-15,-5,1,1,-9,-30,-41,-30,

%T -9,1,1,-14,-49,-77,-77,-49,-14,1,1,-20,-70,-112,-125,-112,-70,-20,1,

%U 1,-27,-90,-126,-117,-117,-126,-90,-27,1,1,-35,-105,-90,45,131,45,-90,-105

%N Generalized Narayana triangle for (-1)^n.

%C Row sums are A139011. Diagonal sums are A180958. Another version is A061176.

%F G.f.: 1/(1-x-xy+x/(1-x-xy))=(1-x(1+y))/(1-2x(1+y)+x^2(1+3y+y^2));

%F E.g.f.: exp((1+y)x)cos(sqrt(y)x);

%F T(n,k)=sum{j=0..n, C(n,j)*C(n-j,2(k-j)*(-1)^(k-j)}.

%e Triangle begins

%e 1,

%e 1, 1,

%e 1, 1, 1,

%e 1, 0, 0, 1,

%e 1, -2, -5, -2, 1,

%e 1, -5, -15, -15, -5, 1,

%e 1, -9, -30, -41, -30, -9, 1,

%e 1, -14, -49, -77, -77, -49, -14, 1,

%e 1, -20, -70, -112, -125, -112, -70, -20, 1,

%e 1, -27, -90, -126, -117, -117, -126, -90, -27, 1,

%e 1, -35, -105, -90, 45, 131, 45, -90, -105, -35, 1

%Y Cf. A056241.

%K easy,sign,tabl

%O 0,12

%A _Paul Barry_, Sep 28 2010

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Last modified October 16 07:30 EDT 2019. Contains 328051 sequences. (Running on oeis4.)