A308536 Expansion of e.g.f. exp(1 - exp(2*x)).

1, -2, 0, 8, 16, -64, -576, -1152, 12800, 136704, 422912, -4464640, -72626176, -413966336, 1805123584, 64448004096, 651340611584, 1132294045696, -73000566390784, -1332193006190592, -10293724166750208, 56984418960539648, 3042980275005947904, 46913652420264329216

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

O.g.f.: 1/(1 + 2*x/(1 - 2*x/(1 + 2*x/(1 - 4*x/(1 + 2*x/(1 - 6*x/(1 + 2*x/(1 - 8*x/(1 + ...))))))))), a continued fraction.

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

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

a(n) = 2^n * A000587(n).

Mathematica

nmax = 23; CoefficientList[Series[Exp[1 - Exp[2x]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = -Sum[2^k Binomial[n - 1, k - 1] a[n - k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]
Table[2^n BellB[n, -1], {n, 0, 23}]

Crossrefs

Cf. A000079, A000587, A009235, A055882, A213170.

Sequence in context: A171552 A087205 A319196 * A241682 A076687 A062134

Adjacent sequences: A308533 A308534 A308535 * A308537 A308538 A308539

Keyword

sign

Author

Ilya Gutkovskiy, Jun 06 2019

Status

approved