A307595 Expansion of e.g.f. (sec(x) + tan(x))*exp(x/(1 - x)).

1, 2, 6, 27, 156, 1097, 9054, 85603, 910840, 10760273, 139634314, 1973272939, 30150497652, 495099175625, 8692428215982, 162444828319579, 3218819701723504, 67394536781529505, 1486511667262146322, 34446575597797488843, 836556499627929889964, 21244918075422301609817

Offset

0,2

Comments

Boustrophedon transform of A000262.

Links

Table of n, a(n) for n=0..21.

Index entries for sequences related to boustrophedon transform

Mathematica

nmax = 21; CoefficientList[Series[(Sec[x] + Tan[x]) Exp[x/(1 - x)], {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := If[n < 1, 1, n! Sum[Binomial[n - 1, j]/(j + 1)!, {j, 0, n - 1}]]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 22, 0]

Prog

(Python)
from itertools import count, islice, accumulate
from sympy import hyper, hyperexpand
def A307595_gen(): # generator of terms
    blist = tuple()
    for i in count(0):
        yield (blist := tuple(accumulate(reversed(blist), initial=hyperexpand(hyper((1-i, -i), [], 1)))))[-1]
A307595_list = list(islice(A307595_gen(), 20)) # Chai Wah Wu, Jun 11 2022

Crossrefs

Cf. A000111, A000262.

Sequence in context: A363456 A118192 A338180 * A058133 A306857 A321584

Adjacent sequences: A307592 A307593 A307594 * A307596 A307597 A307598

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 17 2019

Status

approved