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A125175 Triangle T(n,k) = |A053123(n/2+k/2,k)| for even n+k, T(n,k)= A082985((n+k-1)/2,k) for odd n+k; read by rows, 0<=k<=n. 2
1, 1, 2, 1, 3, 3, 1, 4, 5, 4, 1, 5, 10, 7, 5, 1, 6, 14, 20, 9, 6, 1, 7, 21, 30, 35, 11, 7, 1, 8, 27, 56, 55, 56, 13, 8, 1, 9, 36, 77, 126, 91, 84, 15, 9, 1, 10, 44, 120, 182, 252, 140, 120, 17, 10, 1, 11, 55, 156, 330, 378, 462, 204, 165, 19, 11, 1, 12, 65, 220, 450 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..70.

FORMULA

T(n,k) = binomial(n+1,k) if n+k even. T(n,k) = binomial(n-1,k)*(n+k)/(n-k) if n+k odd. - R. J. Mathar, Sep 08 2013

EXAMPLE

First few rows of the triangle are:

1;

1, 2;

1, 3, 3;

1, 4, 5, 4;

1, 5, 10, 7, 5;

1, 6, 14, 20, 9, 6;

1, 7, 21, 30, 35, 11, 7;

1, 8, 27, 56, 55, 56, 13, 8;

1, 9, 36, 77, 126, 91, 84, 15, 9;

...

MAPLE

A125175 := proc(n, k)

        if type(n+k, 'even') then

                binomial(n+1, k) ;

        else

                binomial(n-1, k)*(n+k)/(n-k) ;

        end if;

end proc: # R. J. Mathar, Sep 08 2013

CROSSREFS

Cf. A053123, A082985, A125176 (row sums).

Sequence in context: A104732 A132108 A210489 * A210552 A193376 A185095

Adjacent sequences:  A125172 A125173 A125174 * A125176 A125177 A125178

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, Nov 22 2006

STATUS

approved

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Last modified March 19 13:37 EDT 2019. Contains 321330 sequences. (Running on oeis4.)