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%I #17 Mar 26 2022 03:53:07
%S 1,3,11,37,123,401,1293,4131,13107,41353,129873,406319,1267093,
%T 3940431,12224579,37845117,116944371,360771417,1111332129,3418840431,
%U 10504903809,32242682787,98863833159,302863592073,927025884477,2835306153351,8665554849903
%N A007318 * A100071.
%C Also A007318^(-1) * A037965. - _Gary W. Adamson_, Nov 10 2007
%F Binomial transform of A100071 starting [1, 2, 6, 12, 30, ...].
%F Inverse binomial transform of A037965 starting [1, 4, 18, 80, 350, ...].
%F a(n) = (n-1)! * [x^(n-1)] exp(x)*((1 + 2*x)*BesselI(0, 2*x) + 2*x*BesselI(1, 2*x)) for n>0, a(0) = 0. - _Peter Luschny_, Aug 26 2012
%F D-finite with recurrence (-n+1)*a(n) +3*(n-1)*a(n-1) +(n+1)*a(n-2) +3*(-n+3)*a(n-3)=0. - _R. J. Mathar_, Nov 09 2021
%e a(3) = 11 = (1, 2, 1) dot (1, 2, 6) = (1 + 4 + 6), where A100071 = (1, 2, 6, 12, 30, ...).
%e a(3) = 11 = (1, -2, 1) dot (1, 4, 18) = (1 - 8 + 18). - _Gary W. Adamson_, Nov 10 2007
%Y Cf. A100071, A037965, A107965.
%K nonn
%O 1,2
%A _Gary W. Adamson_, Nov 08 2007
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