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

%I #9 Jun 11 2022 20:18:16

%S 1,3,10,39,180,977,6156,44401,361872,3295025,33193284,366828033,

%T 4414938000,57501795977,805984165252,12098920460089,193676009792768,

%U 3293501718960033,59294599560573508,1126737323074730161,22536528123718353104,473290909667471110361

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

%C Boustrophedon transform of A000522.

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

%t nmax = 21; CoefficientList[Series[(Sec[x] + Tan[x]) Exp[x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!

%t t[n_, 0] := If[n < 1, 1, Floor[Exp[1] n!]]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 22, 0]

%o (Python)

%o from itertools import count, islice, accumulate

%o def A307593_gen(): # generator of terms

%o blist, m = tuple(), 1

%o for i in count(1):

%o yield (blist := tuple(accumulate(reversed(blist),initial=m)))[-1]

%o m = m*i + 1

%o A307593_list = list(islice(A307593_gen(),30)) # _Chai Wah Wu_, Jun 11 2022

%Y Cf. A000111, A000522, A230960, A307594.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 17 2019