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

%I #31 Apr 16 2019 21:41:19

%S 1,2,6,27,158,1147,9956,100667,1162478,15097487,217833456,3457099107,

%T 59851694498,1122530734327,22672663147556,490646937984347,

%U 11325671204407718,277771419131565167,7213311163322015256,197725569735723642387,5705154145153596656138,172846751677879951716007

%N Expansion of e.g.f. (sec(x) + tan(x))/(2 - exp(x)).

%C Boustrophedon transform of Fubini numbers (A000670).

%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>

%t nmax = 21; CoefficientList[Series[(Sec[x] + Tan[x])/(2 - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!

%t t[n_, 0] := HurwitzLerchPhi[1/2, -n, 0]/2; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 22, 0]

%Y Cf. A000111, A000670, A000764.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 16 2019