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A116407 Triangle whose k-th column has e.g.f. exp(x)*sum{j=0..k, (-1)^j*Bessel_I(k+j,2x)}.

%I A116407 #8 Feb 21 2024 08:18:54
%S A116407 1,1,1,3,1,1,7,3,2,1,19,6,7,3,1,51,15,20,11,4,1,141,36,61,34,16,5,1,
%T A116407 393,91,182,105,55,22,6,1,1107,232,546,314,183,83,29,7,1,3139,603,
%U A116407 1632,930,588,295,119,37,8,1,8953,1585,4875,2727,1858,1001,451,164,46,9,1
%N A116407 Triangle whose k-th column has e.g.f. exp(x)*sum{j=0..k, (-1)^j*Bessel_I(k+j,2x)}.
%C A116407 First column is A002426. Second column is A005043(n+1). Third column is A116408.
%C A116407 Row sums are A116409. Product of A007318 and A116405.
%e A116407 Triangle begins:
%e A116407    1;
%e A116407    1,  1;
%e A116407    3,  1,  1;
%e A116407    7,  3,  2,  1;
%e A116407   19,  6,  7,  3, 1;
%e A116407   51, 15, 20, 11, 4, 1;
%e A116407   ...
%Y A116407 Cf. A002426, A005043, A116408, A116409, A007318, A116405.
%K A116407 easy,nonn,tabl
%O A116407 0,4
%A A116407 _Paul Barry_, Feb 13 2006