A306880 - OEIS

%I #27 Jun 11 2022 20:18:44

%S 1,2,7,44,401,4796,70783,1240448,25146113,578583952,14892958551,

%T 423979878816,13225810908881,448604790288448,16437893908228367,

%U 647074747622534912,27233273311687115649,1220273444664347994368,57998633082360310382119,2914426113026062106334720,154378135436424206699590545

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

%C Boustrophedon transform of A000312.

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

%F a(n) ~ (1 + sin(exp(-1)))/cos(exp(-1)) * n^n. - _Vaclav Kotesovec_, Aug 17 2019

%t nmax = 20; CoefficientList[Series[(Sec[x] + Tan[x])/(1 + LambertW[-x]), {x, 0, nmax}], x] Range[0, nmax]!

%t t[n_, 0] := If[n < 1, 1, n^n]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 21, 0]

%o (Python)

%o from itertools import accumulate, count, islice

%o def A306880_gen(): # generator of terms

%o     blist = tuple()

%o     for i in count(0):

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

%o A306880_list = list(islice(A306880_gen(),30)) # _Chai Wah Wu_, Jun 11 2022

%Y Cf. A000111, A000312, A306881.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 16 2019