A059446 - OEIS

A059446

Triangle T(n,k) = coefficient of x^n*y^k/(n!*k!) in 1/(1-x-y-x*y), read by rows in order 00, 10, 01, 20, 11, 02, ...

1, 1, 1, 2, 3, 2, 6, 10, 10, 6, 24, 42, 52, 42, 24, 120, 216, 300, 300, 216, 120, 720, 1320, 1968, 2268, 1968, 1320, 720, 5040, 9360, 14640, 18576, 18576, 14640, 9360, 5040, 40320, 75600, 122400, 166320, 184896, 166320, 122400, 75600, 40320

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..44.

FORMULA

E.g.f.: 1/(1-x-y-x*y).

T(n, k) = n!*2^k*Hypergeometric2F1([-k, -k], [-n], 1/2). - Detlef Meya, Aug 18 2024

EXAMPLE

Triangle begins:

1,1;

2,3,2;

6,10,10,6;

...

MAPLE

read transforms; SERIES2(1/(1-x-y-x*y), x, y, 12): SERIES2TOLISTMULT(%, x, y, 12);

MATHEMATICA

T[n_, k_] := n!*2^k*Hypergeometric2F1[-k, -k, -n, 1/2]; Table[T[n, k], {n, 0, 8}, {k, 0, n}]//Flatten (* Detlef Meya, Aug 18 2024 *)

CROSSREFS

Cf. A008288.

Sequence in context: A025502 A110777 A087454 * A298854 A355266 A188881

Adjacent sequences: A059443 A059444 A059445 * A059447 A059448 A059449

KEYWORD

nonn,tabl,easy

AUTHOR

N. J. A. Sloane, Feb 02 2001

STATUS

approved