A337444 - OEIS

%I #9 Jun 11 2022 14:03:23

%S 1,2,0,-1,-8,-5,-50,79,-696,3375,-22830,156719,-1205244,9952735,

%T -88770370,847488719,-8633147152,93430030975,-1070638898070,

%U 12950169210479,-164886839860420,2204373939190495,-30873660197736330,452059981437456399,-6906967824497129048

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

%C Inverse boustrophedon transform of odd numbers.

%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * (2*k+1) * A000111(n-k).

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

%t 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}]

%o (Python)

%o from itertools import count, islice, accumulate

%o from operator import sub

%o def A337444_gen(): # generator of terms

%o     blist = tuple()

%o     for i in count(1,2):

%o         yield (blist := tuple(accumulate(reversed(blist),func=sub,initial=i)))[-1]

%o A337444_list = list(islice(A337444_gen(),30)) # _Chai Wah Wu_, Jun 11 2022

%Y Cf. A000111, A000754, A005408.

%K sign

%O 0,2

%A _Ilya Gutkovskiy_, Aug 27 2020