A368487 - OEIS

%I #14 Dec 27 2023 07:45:21

%S 1,1,1,1,2,1,1,5,3,1,1,10,17,4,1,1,17,64,49,5,1,1,26,177,334,129,6,1,

%T 1,37,401,1457,1549,321,7,1,1,50,793,4776,10417,6652,769,8,1,1,65,

%U 1422,12889,48526,67761,27064,1793,9,1,1,82,2369,30234,176185,442276,411825,105796,4097,10,1

%N Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} k^j * binomial(j+k-1,j).

%F G.f. of column k: 1/((1-x) * (1-k*x)^k).

%e Square array begins:

%e   1, 1,   1,    1,     1,      1, ...

%e   1, 2,   5,   10,    17,     26, ...

%e   1, 3,  17,   64,   177,    401, ...

%e   1, 4,  49,  334,  1457,   4776, ...

%e   1, 5, 129, 1549, 10417,  48526, ...

%e   1, 6, 321, 6652, 67761, 442276, ...

%o (PARI) T(n, k) = sum(j=0, n, k^j*binomial(j+k-1, j));

%Y Columns k=0..3 give A000012, A000027(n+1), A000337(n+1), A367591.

%Y Main diagonal gives A368488.

%Y Cf. A119258, A368486.

%K nonn,tabl,easy

%O 0,5

%A _Seiichi Manyama_, Dec 26 2023