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A296792 Expansion of e.g.f. (sec(x) + tan(x))/sqrt(1 - 2*x).

%I A296792 #19 Jun 11 2022 20:05:46
%S A296792 1,2,6,29,196,1721,18622,239427,3563880,60247537,1139848346,
%T A296792 23857033243,547234058732,13650416199369,367871731383990,
%U A296792 10651249531927427,329733427896399952,10868107639700229857,379980639501713082034,14046060369812427842859,547335961798415004947220
%N A296792 Expansion of e.g.f. (sec(x) + tan(x))/sqrt(1 - 2*x).
%C A296792 Boustrophedon transform of A001147.
%H A296792 Robert Israel, <a href="/A296792/b296792.txt">Table of n, a(n) for n = 0..403</a>
%H A296792 J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A (1996), 44-54 (<a href="http://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>)
%H A296792 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A296792 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%H A296792 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A296792 a(n) ~ (sec(1/2) + tan(1/2)) * 2^(n + 1/2) * n^n / exp(n). - _Vaclav Kotesovec_, Dec 21 2017
%p A296792 S:= series((sec(x)+tan(x))/sqrt(1-2*x), x, 51):
%p A296792 seq(coeff(S,x,n)*n!,n=0..50); # _Robert Israel_, Dec 21 2017
%t A296792 nmax = 20; CoefficientList[Series[(Sec[x] + Tan[x])/Sqrt[1 - 2 x], {x, 0, nmax}], x] Range[0, nmax]!
%o A296792 (PARI) first(n) = x='x+O('x^n); Vec(serlaplace((1/cos(x) + tan(x))/sqrt(1-2*x))) \\ _Iain Fox_, Dec 21 2017
%o A296792 (Python)
%o A296792 from itertools import accumulate, count, islice
%o A296792 def A296792_gen(): # generator of terms
%o A296792     blist, m = tuple(), 1
%o A296792     for i in count(1,2):
%o A296792         yield (blist := tuple(accumulate(reversed(blist),initial=m)))[-1]
%o A296792         m *= i
%o A296792 A296792_list = list(islice(A296792_gen(),30)) # _Chai Wah Wu_, Jun 11 2022
%Y A296792 Cf. A000111, A000754, A001147, A230960, A230961.
%K A296792 nonn
%O A296792 0,2
%A A296792 _Ilya Gutkovskiy_, Dec 20 2017