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Triangle whose k-th column has e.g.f. exp(x)*sum{j=0..k, Bessel_I(k+j,2x)}.
1

%I #9 Feb 21 2024 08:18:50

%S 1,1,1,3,3,1,7,9,4,1,19,26,15,5,1,51,75,50,21,6,1,141,216,161,78,28,7,

%T 1,393,623,504,273,113,36,8,1,1107,1800,1554,918,423,157,45,9,1,3139,

%U 5211,4740,3006,1506,625,211,55,10,1,8953,15115,14355,9657,5182,2343,891,276

%N Triangle whose k-th column has e.g.f. exp(x)*sum{j=0..k, Bessel_I(k+j,2x)}.

%C First column is A002426. Second column is A005774. Third column is A014532.

%e Triangle begins:

%e 1,

%e 1, 1,

%e 3, 3, 1,

%e 7, 9, 4, 1,

%e 19, 26, 15, 5, 1,

%e 51, 75, 50, 21, 6, 1

%e ...

%Y Cf. A002426, A005774, A014532.

%K easy,nonn,tabl

%O 0,4

%A _Paul Barry_, Feb 13 2006