A320904 T(n, k) = binomial(2*n + 1 - k, k)*hypergeom([1, 1, -k], [1, 2*(n - k + 1)], -1), triangle read by rows, T(n, k) for n >= 0 and 0 <= k <= n.

1, 1, 3, 1, 5, 7, 1, 7, 16, 15, 1, 9, 29, 42, 31, 1, 11, 46, 93, 99, 63, 1, 13, 67, 176, 256, 219, 127, 1, 15, 92, 299, 562, 638, 466, 255, 1, 17, 121, 470, 1093, 1586, 1486, 968, 511, 1, 19, 154, 697, 1941, 3473, 4096, 3302, 1981, 1023

Offset

0,3

Links

Table of n, a(n) for n=0..54.

Example

Triangle starts:
[0] 1
[1] 1,  3
[2] 1,  5,   7
[3] 1,  7,  16,  15
[4] 1,  9,  29,  42,   31
[5] 1, 11,  46,  93,   99,   63
[6] 1, 13,  67, 176,  256,  219,  127
[7] 1, 15,  92, 299,  562,  638,  466, 255
[8] 1, 17, 121, 470, 1093, 1586, 1486, 968, 511

Maple

T := (n, k) -> binomial(2*n + 1 - k, k)*hypergeom([1, 1, -k], [1, 2*(n-k+1)], -1):
for n from 0 to 11 do seq(simplify(T(n, k)), k = 0..n) od;

Mathematica

s={}; For[n=0, n<19, n++, For[k=0, k<n+1, k++, AppendTo[s, 2^(2*n+1-k)-Sum[Binomial[2*n+1-k, i], {i, 0, 2*n+1-2*k-1}]]]]; s (* Detlef Meya, Oct 03 2023 *)

Crossrefs

Row sums are A105693(n-1).

Cf. A097750.

Sequence in context: A221881 A201811 A199898 * A193844 A201552 A216182

Adjacent sequences: A320901 A320902 A320903 * A320905 A320906 A320907

Keyword

nonn,tabl

Author

Peter Luschny, Oct 28 2018

Status

approved