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URL: https://oeis.org/A306880

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A306880
Expansion of e.g.f. (sec(x) + tan(x))/(1 + LambertW(-x)).
2
1, 2, 7, 44, 401, 4796, 70783, 1240448, 25146113, 578583952, 14892958551, 423979878816, 13225810908881, 448604790288448, 16437893908228367, 647074747622534912, 27233273311687115649, 1220273444664347994368, 57998633082360310382119, 2914426113026062106334720, 154378135436424206699590545
OFFSET
0,2
COMMENTS
Boustrophedon transform of A000312.
FORMULA
a(n) ~ (1 + sin(exp(-1)))/cos(exp(-1)) * n^n. - Vaclav Kotesovec, Aug 17 2019
MATHEMATICA
nmax = 20; CoefficientList[Series[(Sec[x] + Tan[x])/(1 + LambertW[-x]), {x, 0, nmax}], x] Range[0, nmax]!
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]
PROG
(Python)
from itertools import accumulate, count, islice
def A306880_gen(): # generator of terms
blist = tuple()
for i in count(0):
yield (blist := tuple(accumulate(reversed(blist), initial=i**i)))[-1]
A306880_list = list(islice(A306880_gen(), 30)) # Chai Wah Wu, Jun 11 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 16 2019
STATUS
approved