A292631 - OEIS

%I #8 Sep 20 2017 20:01:52

%S 1,2,10,75,758,9660,148772,2688420,55784710,1307378358,34158527852,

%T 984547901051,31034429035260,1062081192039140,39218355263626632,

%U 1554260970293874135,65803396940022289734,2964120950479432183950,141548149894016562758300,7143010414313948156920665,379821534884560034711455956

%N a(n) = n! * [x^n] exp(n*x)*(BesselI(0,2*x) + BesselI(1,2*x)).

%C The n-th term of the n-th binomial transform of A001405.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F a(n) = A292630(n,n).

%F a(n) ~ (BesselI(0,2) + BesselI(1,2)) * n^n. - _Vaclav Kotesovec_, Sep 20 2017

%t Table[n!*SeriesCoefficient[E^(n*x)*(BesselI[0,2*x] + BesselI[1,2*x]),{x,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Sep 20 2017 *)

%Y Main diagonal of A292630.

%Y Cf. A001405, A186925, A292629, A292632.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Sep 20 2017