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A180957 Generalized Narayana triangle for (-1)^n. 1
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, -9, 1, 1, -14, -49, -77, -77, -49, -14, 1, 1, -20, -70, -112, -125, -112, -70, -20, 1, 1, -27, -90, -126, -117, -117, -126, -90, -27, 1, 1, -35, -105, -90, 45, 131, 45, -90, -105 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

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

LINKS

Table of n, a(n) for n=0..63.

FORMULA

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

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

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

EXAMPLE

Triangle begins

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, -9, 1,

1, -14, -49, -77, -77, -49, -14, 1,

1, -20, -70, -112, -125, -112, -70, -20, 1,

1, -27, -90, -126, -117, -117, -126, -90, -27, 1,

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

CROSSREFS

Cf. A056241.

Sequence in context: A320032 A270061 A061176 * A124780 A108437 A226029

Adjacent sequences:  A180954 A180955 A180956 * A180958 A180959 A180960

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Sep 28 2010

STATUS

approved

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Last modified September 19 23:31 EDT 2019. Contains 327207 sequences. (Running on oeis4.)