A216182 Riordan array ((1+x)/(1-x)^2, x(1+x)^2/(1-x)^2).

1, 3, 1, 5, 7, 1, 7, 25, 11, 1, 9, 63, 61, 15, 1, 11, 129, 231, 113, 19, 1, 13, 231, 681, 575, 181, 23, 1, 15, 377, 1683, 2241, 1159, 265, 27, 1, 17, 575, 3653, 7183, 5641, 2047, 365, 31, 1, 19, 833, 7183, 19825, 22363, 11969, 3303, 481, 35, 1

Offset

0,2

Comments

Triangle formed of odd-numbered columns of the Delannoy triangle A008288.

Links

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Formula

T(2n, n) = A108448(n+1).

Sum_{k=0..n} T(n,k) = A073717(n+1).

From G. C. Greubel, Nov 19 2021: (Start)

T(n, k) = A008288(n+k+1, 2*k+1).

T(n, k) = hypergeometric([-n+k, -2*k-1], [1], 2). (End)

Example

Triangle begins
   1;
   3,   1;
   5,   7,    1;
   7,  25,   11,    1;
   9,  63,   61,   15,    1;
  11, 129,  231,  113,   19,    1;
  13, 231,  681,  575,  181,   23,   1;
  15, 377, 1683, 2241, 1159,  265,  27,  1;
  17, 575, 3653, 7183, 5641, 2047, 365, 31, 1;
  ...

Mathematica

A216182[n_, k_]:= Hypergeometric2F1[-n +k, -2*k-1, 1, 2];
Table[A216182[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 19 2021 *)

Prog

(Sage)
def A216182(n, k): return simplify( hypergeometric([-n+k, -2*k-1], [1], 2) )
flatten([[A216182(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Nov 19 2021

Crossrefs

Cf. (columns:) A005408, A001845, A001847, A001849, A008419.

Cf. Diagonals: A000012, A004767, A060820.

Cf. A008288 (Delannoy triangle), A114123 (even-numbered columns of A008288).

Sequence in context: A320904 A193844 A201552 * A143524 A134249 A188509

Adjacent sequences: A216179 A216180 A216181 * A216183 A216184 A216185

Keyword

nonn,tabl

Author

Philippe Deléham, Mar 11 2013

Status

approved