

A297191


Irregular triangle read by rows formed by taking every other row of the Delannoy array (A008288) regarded as a triangle.


3



1, 1, 3, 1, 1, 7, 13, 7, 1, 1, 11, 41, 63, 41, 11, 1, 1, 15, 85, 231, 321, 231, 85, 15, 1, 1, 19, 145, 575, 1289, 1683, 1289, 575, 145, 19, 1, 1, 23, 221, 1159, 3649, 7183, 8989, 7183, 3649, 1159, 221, 23, 1, 1, 27, 313, 2047, 8361, 22363, 40081, 48639, 40081
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OFFSET

0,3


LINKS



FORMULA

T(n, k) = (1)^k*hypergeometric2F1([2*n+k, k+1], [1], 2) for 0 <= k <= 2*n.
Sum_{k=0..2*n} T(n,k) = A000129(2*n+1). (End)


EXAMPLE

The Delannoy triangle (A008288) begins:
1;
1, 1;
1, 3, 1;
1, 5, 5, 1;
1, 7, 13, 7, 1;
1, 9, 25, 25, 9, 1;
1, 11, 41, 63, 41, 11, 1;
1, 13, 61, 129, 129, 61, 13, 1;
1, 15, 85, 231, 321, 231, 85, 15, 1;
1, 17, 113, 377, 681, 681, 377, 113, 17, 1;
this irregular triangle begins:
1;
1, 3, 1;
1, 7, 13, 7, 1;
1, 11, 41, 63, 41, 11, 1;
1, 15, 85, 231, 321, 231, 85, 15, 1;
1, 19, 145, 575, 1289, 1683, 1289, 575, 145, 19, 1;
...


MATHEMATICA

A297191[n_, k_]:= (1)^k*Hypergeometric2F1[2*n+k, k+1, 1, 2];


PROG

(PARI) See Links section.
(Sage)
def A297191(n, k): return (1)^k*hypergeometric([2*n+k, k+1], [1], 2).simplify()


CROSSREFS



KEYWORD

nonn,tabf,easy


AUTHOR



EXTENSIONS



STATUS

approved



