A367784 a(n) = exp(1) * Sum_{k>=0} (-1)^k * (n*k - 1)^n / k!.

1, -2, 5, 17, 17, -8151, -311435, -777974, 927723585, 82906687673, 1693962380101, -707005824990631, -137258747025993071, -10253960705018807830, 1697644859939460151413, 803696888217607331079149, 148126297324647875348070657, -323461353221296480463456191

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = n! * [x^n] exp(1 - x - exp(n*x)).

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

Mathematica

Table[n! SeriesCoefficient[Exp[1 - x - Exp[n x]], {x, 0, n}], {n, 0, 17}]
Unprotect[Power]; 0^0 = 1; Table[Sum[(-1)^(n - k) Binomial[n, k] n^k BellB[k, -1], {k, 0, n}], {n, 0, 17}]

Crossrefs

Cf. A000587, A109747, A307066, A307080, A330605, A367743, A367744.

Sequence in context: A276767 A123364 A247857 * A025553 A343775 A075544

Adjacent sequences: A367781 A367782 A367783 * A367785 A367786 A367787

Keyword

sign

Author

Ilya Gutkovskiy, Nov 30 2023

Status

approved