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A292976 a(n) = n! * [x^n] exp(n*x)*(sec(x) + tan(x)).

%I A292976 #11 Dec 09 2018 12:15:40
%S A292976 1,2,9,65,645,8141,124729,2247853,46584937,1091386465,28521016621,
%T A292976 822514469149,25946988879053,888784357214729,32851731018695905,
%U A292976 1303291334592451037,55235983848811714129,2490726416399046168993,119065442891277782378581,6014589653389306889686941
%N A292976 a(n) = n! * [x^n] exp(n*x)*(sec(x) + tan(x)).
%H A292976 Alois P. Heinz, <a href="/A292976/b292976.txt">Table of n, a(n) for n = 0..386</a>
%H A292976 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A292976 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A292976 a(n) = A292975(n,n).
%F A292976 a(n) ~ (1 + sin(1)) / cos(1) * n^n. - _Vaclav Kotesovec_, Oct 06 2017
%p A292976 b:= proc(u, o) option remember; `if`(u+o=0, 1,
%p A292976       add(b(o-1+j, u-j), j=1..u))
%p A292976     end:
%p A292976 A:= proc(n, k) option remember; `if`(k=0, b(n, 0),
%p A292976       add(binomial(n, j)*A(j, k-1), j=0..n))
%p A292976     end:
%p A292976 a:= n-> A(n$2):
%p A292976 seq(a(n), n=0..20);  # _Alois P. Heinz_, Sep 27 2017
%t A292976 Table[n! SeriesCoefficient[Exp[n x] (Sec[x] + Tan[x]), {x, 0, n}], {n, 0, 20}]
%Y A292976 Main diagonal of A292975.
%Y A292976 Cf. A000111.
%K A292976 nonn
%O A292976 0,2
%A A292976 _Ilya Gutkovskiy_, Sep 27 2017