A367743 Expansion of e.g.f. exp(1 - x - exp(2*x)).

1, -3, 5, 1, -7, -75, -99, 1241, 10161, 18989, -332299, -3857551, -14440151, 141168997, 2807256333, 20182451657, -42073176479, -2999363709091, -38439478980891, -161835672017439, 3439471815545177, 87228227501354517, 937579822282327421, 216540362854403513, -198501712690150659055

Offset

0,2

Links

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

Formula

a(n) = exp(1) * Sum_{k>=0} (-1)^k * (2*k-1)^n / k!.

a(0) = 1; a(n) = -a(n-1) - Sum_{k=1..n} binomial(n-1,k-1) * 2^k * a(n-k).

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * 2^k * A000587(k).

Mathematica

nmax = 24; CoefficientList[Series[Exp[1 - x - Exp[2 x]], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -a[n - 1] - Sum[Binomial[n - 1, k - 1] 2^k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]
Table[Sum[(-1)^(n - k) Binomial[n, k] 2^k BellB[k, -1], {k, 0, n}], {n, 0, 24}]

Crossrefs

Cf. A000587, A004211, A009235, A109747, A124311, A126390, A308536, A308645, A367744.

Sequence in context: A353413 A318190 A289714 * A242390 A065395 A236631

Adjacent sequences: A367740 A367741 A367742 * A367744 A367745 A367746

Keyword

sign

Author

Ilya Gutkovskiy, Nov 29 2023

Status

approved