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A180960 A generalized Narayana triangles for sec(x)^2 (or Zag numbers). 0
1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 16, 46, 16, 1, 1, 25, 150, 150, 25, 1, 1, 36, 375, 952, 375, 36, 1, 1, 49, 791, 4039, 4039, 791, 49, 1, 1, 64, 1484, 12992, 31078, 12992, 1484, 64, 1, 1, 81, 2556, 34524, 162774, 162774, 34524, 2556, 81, 1, 1, 100, 4125, 79920, 641250 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..59.

FORMULA

G.f.: 1/(1-x-xy-1*2*x^2y/(1-x-xy-2*3*x^2y/(1-x-xy-3*4*x^2y/(1-...(continued fraction);

E.g.f.: exp((1+y)x)*sec^2(sqrt(y)x);

T(n,k)=sum{j=0..n, C(n,j)*C(n-j,2(k-j))*Z_(k-j)}, Z_n=A000182(n+1).

EXAMPLE

Triangle begins

1,

1, 1,

1, 4, 1,

1, 9, 9, 1,

1, 16, 46, 16, 1,

1, 25, 150, 150, 25, 1,

1, 36, 375, 952, 375, 36, 1,

1, 49, 791, 4039, 4039, 791, 49, 1,

1, 64, 1484, 12992, 31078, 12992, 1484, 64, 1,

1, 81, 2556, 34524, 162774, 162774, 34524, 2556, 81, 1,

1, 100, 4125, 79920, 641250, 1484504, 641250, 79920, 4125, 100, 1

CROSSREFS

Cf. A180959.

Sequence in context: A124216 A008459 A259333 * A157192 A154982 A146767

Adjacent sequences:  A180957 A180958 A180959 * A180961 A180962 A180963

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Sep 28 2010

STATUS

approved

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Last modified September 21 13:37 EDT 2019. Contains 327253 sequences. (Running on oeis4.)