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%I #14 Mar 10 2023 16:30:58
%S 1,2,36,1860,190120,32232060,8175770064,2898980908824,
%T 1369263687414480,830988068906518380,630109741730668410640,
%U 583773362067938664133512,648851848280206013365243776,852146184628067383511375555000,1305460597778526044143501996708800,2307324514460203126471248458864413200
%N a(n) = (2*n)! * [x^(2*n)] BesselI(0,2*x)^n.
%H Alois P. Heinz, <a href="/A303503/b303503.txt">Table of n, a(n) for n = 0..212</a>
%F a(n) = A287318(n,n).
%F a(n) ~ c * d^n * n^(2*n), where c = 1.72802011936236389522137050964080... and d = 1.1381284656425793765251319541847869000364101065484286935... - _Vaclav Kotesovec_, Apr 26 2018
%F a(n) = A000984(n)*A033935(n). - _Alois P. Heinz_, Jan 30 2023
%p b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
%p add(b(n-j, i-1)*binomial(n, j)^2, j=0..n))
%p end:
%p a:= n-> (2*n)!*b(n$2)/n!^2:
%p seq(a(n), n=0..17); # _Alois P. Heinz_, Jan 29 2023
%t Table[(2 n)! SeriesCoefficient[BesselI[0, 2 x]^n, {x, 0, 2 n}], {n, 0, 15}]
%Y Main diagonal of A287318.
%Y Cf. A000984, A002894, A002896, A033935, A039699, A287317, A361297.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Apr 25 2018
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