A340554 T(n, k) = [x^k] hypergeom([-2^n/2, -2^n/2 - 1/2], [1/2], x). Triangle read by rows, T(n, k) for n >= 0.

1, 1, 1, 3, 1, 10, 5, 1, 36, 126, 84, 9, 1, 136, 2380, 12376, 24310, 19448, 6188, 680, 17, 1, 528, 40920, 1107568, 13884156, 92561040, 354817320, 818809200, 1166803110, 1037158320, 573166440, 193536720, 38567100, 4272048, 237336, 5456, 33

Offset

0,4

Links

Table of n, a(n) for n=0..37.

Example

Triangle starts:
                           [0] 1, 1
                           [1] 1, 3
                         [2] 1, 10, 5
                     [3] 1, 36, 126, 84, 9
     [4] 1, 136, 2380, 12376, 24310, 19448, 6188, 680, 17

Maple

CoeffList := p -> op(PolynomialTools:-CoefficientList(p, x)):
Tpoly := proc(n) simplify(hypergeom([-2^n/2, -2^n/2 - 1/2], [1/2], x)):
CoeffList(%) end: seq(Tpoly(n), n = 0..5);

Mathematica

Tpoly[n_] := HypergeometricPFQ[{-2^n/2, -2^n/2 - 1/2}, {1/2}, x];
Table[CoefficientList[Tpoly[n], x], {n, 0, 5}] // Flatten

Crossrefs

Cf. A001146 (row sums), A000051 (main diagonal), A016131 (central terms), A201461, A028297.

Sequence in context: A091042 A111418 A113187 * A057967 A347258 A132964

Adjacent sequences: A340551 A340552 A340553 * A340555 A340556 A340557

Keyword

nonn,tabf

Author

Peter Luschny, Feb 03 2021

Status

approved