A337447 E.g.f.: exp(exp(x) - 1) / (sec(x) + tan(x)).

1, 0, 1, 0, 4, -4, 31, -144, 379, -5560, 8572, -263128, 473485, -15744416, 47003477, -1206879556, 5944492012, -119190424496, 876847239971, -15100821637664, 149690044061351, -2416631748015804, 29675481449346820, -477579212590451988, 6840036862556737337

Offset

0,5

Comments

Inverse boustrophedon transform of Bell numbers.

Links

Table of n, a(n) for n=0..24.

Index entries for sequences related to boustrophedon transform

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A000110(k) * A000111(n-k).

Mathematica

nmax = 24; CoefficientList[Series[Exp[Exp[x] - 1]/(Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := BellB[n]; t[n_, k_] := t[n, k] = t[n, k - 1] - t[n - 1, n - k]; a[n_] := t[n, n]; Table[a[n], {n, 0, 24}]

Prog

(Python)
from itertools import islice, accumulate
from operator import sub
def A337447_gen(): # generator of terms
    yield from (1, 0)
    blist, alist = (1, 0), (1, )
    while True:
        yield (blist := tuple(accumulate(reversed(blist), func=sub, initial=(alist := list(accumulate(alist, initial=alist[-1])))[-1])))[-1]
A337447_list = list(islice(A337447_gen(), 30)) # Chai Wah Wu, Jun 11-12 2022

Crossrefs

Cf. A000110, A000111, A000764.

Sequence in context: A348635 A307499 A111723 * A239601 A196131 A256691

Adjacent sequences: A337444 A337445 A337446 * A337448 A337449 A337450

Keyword

sign

Author

Ilya Gutkovskiy, Aug 27 2020

Status

approved