A336958 E.g.f.: 1 / (exp(2*x) - x).

1, -1, -2, 10, 24, -312, -560, 19472, 6272, -1994624, 4072704, 299059968, -1635814400, -60723321856, 628215191552, 15716076562432, -274420622327808, -4900668238036992, 140182198527655936, 1717697481518809088, -83651335147070685184, -590374211868638314496

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

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

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

Mathematica

nmax = 21; CoefficientList[Series[1/(Exp[2 x] - x), {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[(-2 (n - k + 1))^k/k!, {k, 0, n}], {n, 0, 21}]
a[0] = 1; a[n_] := a[n] = -n a[n - 1] - Sum[Binomial[n, k] 2^k a[n - k], {k, 2, n}]; Table[a[n], {n, 0, 21}]

Crossrefs

Cf. A089148, A336947, A336959.

Sequence in context: A270822 A248117 A345695 * A305600 A058373 A167386

Adjacent sequences: A336955 A336956 A336957 * A336959 A336960 A336961

Keyword

sign

Author

Ilya Gutkovskiy, Aug 09 2020

Status

approved