%I #5 Jan 25 2022 21:40:13

%S 1,1,1,1,2,2,1,3,6,5,1,4,12,20,14,1,5,20,50,70,43,1,6,30,100,210,258,

%T 143,1,7,42,175,490,903,1001,509,1,8,56,280,980,2408,4004,4072,1922,1,

%U 9,72,420,1764,5418,12012,18324,17298,7651

%N Triangle read by rows, A007318 * A153198.

%C Row sums = A153197 starting (1, 2, 5, 15, 51, 189, 748, 3138,...).

%C Right border = A006789: (1, 1, 2, 5, 14, 43, 143, 509, 1922,...).

%F Binomial transform of triangle A153198, where A153198 = an infinite lower triangular matrix with the Bessel numbers A006789 as the main diagonal and the rest 0's.

%e First few rows of the triangle =

%e 1;

%e 1, 1;

%e 1, 2, 2;

%e 1, 3, 6, 5;

%e 1, 4, 12, 20, 14;

%e 1, 5, 20, 50, 70, 43;

%e 1, 6, 30, 100, 210, 258, 143;

%e 1, 7, 42, 175, 490, 903, 1001, 509;

%e 1, 8, 56, 280, 980, 2408, 4004, 4072, 1922;

%e 1, 9, 72, 420, 1764, 5418, 12012, 18324, 17298, 7651;

%e 1, 10, 90, 600, 2940, 10836, 30030, 61080, 86490, 76510, 31965;

%e ...

%Y Cf. A153197, A153198, A006789.

%K nonn,tabl

%O 0,5

%A _Gary W. Adamson_, Dec 20 2008