A306880 Expansion of e.g.f. (sec(x) + tan(x))/(1 + LambertW(-x)).

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.

Links

Table of n, a(n) for n=0..20.

Index entries for sequences related to boustrophedon transform

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

Cf. A000111, A000312, A306881.

Sequence in context: A178012 A194018 A196793 * A128579 A194453 A346258

Adjacent sequences: A306877 A306878 A306879 * A306881 A306882 A306883

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 16 2019

Status

approved