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A180959 Generalized Narayana triangle for secant. 1
1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 23, 10, 1, 1, 15, 65, 65, 15, 1, 1, 21, 150, 321, 150, 21, 1, 1, 28, 301, 1197, 1197, 301, 28, 1, 1, 36, 546, 3584, 7531, 3584, 546, 36, 1, 1, 45, 918, 9114, 35523, 35523, 9114, 918, 45, 1, 1, 55, 1455, 20490, 132045, 276433, 132045 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..61.

FORMULA

G.f.: 1/(1-x-xy-x^2y/(1-x-xy-4x^2y/(1-x-xy-9x^2y/(1-...(continued fraction);

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

T(n,k)=sum{j=0..n, C(n,j)*C(n-j,2(k-j))*E_(k-j)}, E_n=A000364(n).

EXAMPLE

Triangle begins

1,

1, 1,

1, 3, 1,

1, 6, 6, 1,

1, 10, 23, 10, 1,

1, 15, 65, 65, 15, 1,

1, 21, 150, 321, 150, 21, 1,

1, 28, 301, 1197, 1197, 301, 28, 1,

1, 36, 546, 3584, 7531, 3584, 546, 36, 1,

1, 45, 918, 9114, 35523, 35523, 9114, 918, 45, 1,

1, 55, 1455, 20490, 132045, 276433, 132045, 20490, 1455, 55, 1

CROSSREFS

Sequence in context: A088925 A100862 A098568 * A131235 A202812 A157243

Adjacent sequences:  A180956 A180957 A180958 * A180960 A180961 A180962

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Sep 28 2010

STATUS

approved

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Last modified September 15 16:42 EDT 2019. Contains 327078 sequences. (Running on oeis4.)