A306881 Expansion of e.g.f. -(sec(x) + tan(x))*LambertW(-x).

0, 1, 4, 18, 120, 1100, 13092, 192360, 3362128, 68063760, 1565077220, 40275499264, 1146522753288, 35767031711424, 1213309504953028, 44464470056979840, 1750597156059648544, 73688248937813125376, 3302340234016493521476, 156980994639584475390976, 7889413937606432287327000

Offset

0,3

Comments

Boustrophedon transform of A000169.

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-1). - Vaclav Kotesovec, Aug 17 2019

Mathematica

nmax = 20; CoefficientList[Series[-(Sec[x] + Tan[x]) LambertW[-x], {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := If[n < 1, 0, n^(n - 1)]; 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 count, islice, accumulate
def A306881_gen(): # generator of terms
    yield 0
    blist = (0, )
    for i in count(1):
        yield (blist := tuple(accumulate(reversed(blist), initial=i**(i-1))))[-1]
A306881_list = list(islice(A306881_gen(), 30)) # Chai Wah Wu, Jun 11 2022

Crossrefs

Cf. A000111, A000169, A306880.

Sequence in context: A222375 A053529 A005442 * A367489 A084661 A112294

Adjacent sequences: A306878 A306879 A306880 * A306882 A306883 A306884

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 16 2019

Status

approved