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A101603 Riordan array (1/(1-x^2),x(1+x)/(1-x)). 3
1, 0, 1, 1, 2, 1, 0, 3, 4, 1, 1, 4, 9, 6, 1, 0, 5, 16, 19, 8, 1, 1, 6, 25, 44, 33, 10, 1, 0, 7, 36, 85, 96, 51, 12, 1, 1, 8, 49, 146, 225, 180, 73, 14, 1, 0, 9, 64, 231, 456, 501, 304, 99, 16, 1, 1, 10, 81, 344, 833, 1182, 985, 476, 129, 18, 1, 0, 11, 100, 489, 1408, 2471, 2668 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are A097076(n+1). Diagonal sums are abs(A077902).

LINKS

Table of n, a(n) for n=0..72.

FORMULA

Number triangle whose columns are generated by x^k*(1+x)^(k-1)/(1-x)^(k+1)

Number triangle T(n, k)=sum{j=0..n-k, C(k-1, j)C(n-j, n-k-j)};

EXAMPLE

Rows start

1;

0,1;

1,2,1;

0,3,4,1;

1,4,9,6,1;

0,5,16,19,8,1;

MATHEMATICA

t[n_, k_] := Binomial[n+k, k]*Hypergeometric2F1[-k+1, -n, -n-k, -1]; Table[t[n-k, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Nov 22 2013 *)

CROSSREFS

Cf. A119328 (row-reversed).

Sequence in context: A256130 A257566 A188286 * A228161 A124030 A166040

Adjacent sequences:  A101600 A101601 A101602 * A101604 A101605 A101606

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Dec 08 2004

STATUS

approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)