A337444 Expansion of e.g.f. (1 + 2*x) * exp(x) / (sec(x) + tan(x)).

1, 2, 0, -1, -8, -5, -50, 79, -696, 3375, -22830, 156719, -1205244, 9952735, -88770370, 847488719, -8633147152, 93430030975, -1070638898070, 12950169210479, -164886839860420, 2204373939190495, -30873660197736330, 452059981437456399, -6906967824497129048

Offset

0,2

Comments

Inverse boustrophedon transform of odd 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) * (2*k+1) * A000111(n-k).

Mathematica

nmax = 24; CoefficientList[Series[(1 + 2 x) Exp[x]/(Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := 2 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}]

Prog

(Python)
from itertools import count, islice, accumulate
from operator import sub
def A337444_gen(): # generator of terms
    blist = tuple()
    for i in count(1, 2):
        yield (blist := tuple(accumulate(reversed(blist), func=sub, initial=i)))[-1]
A337444_list = list(islice(A337444_gen(), 30)) # Chai Wah Wu, Jun 11 2022

Crossrefs

Cf. A000111, A000754, A005408.

Sequence in context: A278881 A335095 A344069 * A340556 A201637 A055141

Adjacent sequences: A337441 A337442 A337443 * A337445 A337446 A337447

Keyword

sign

Author

Ilya Gutkovskiy, Aug 27 2020

Status

approved