A337443 E.g.f.: (1 + x) * exp(x) / (sec(x) + tan(x)).

1, 1, 0, -1, -4, -5, -20, 9, -208, 855, -6180, 41549, -321792, 2651155, -23664420, 225865769, -2301032256, 24901626095, -285356879940, 3451591584869, -43947119045600, 587529302036875, -8228722825167940, 120487046847246049, -1840906518665985824

Offset: 0

Author

Ilya Gutkovskiy, Aug 27 2020

Keywords

• sign

Comments

Inverse boustrophedon transform of positive natural numbers.

Links

• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A000027, A000111, A000737, A034428, A231179.

Programs

Mathematica

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

Python

from itertools import count, islice, accumulate
from operator import sub
def A337443_gen(): # generator of terms
    blist = tuple()
    for i in count(1):
        yield (blist := tuple(accumulate(reversed(blist),func=sub,initial=i)))[-1]
A337443_list = list(islice(A337443_gen(),30)) # Chai Wah Wu, Jun 11 2022

Formula

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