A308646 a(n) = exp(1) * Sum_{k>=0} (-1)^k*k^(2*n)/k!.

1, 0, 1, -9, 50, 413, -17731, 110176, 9938669, -278475061, -9816860358, 725503033401, 15823587507881, -2848115497132448, -38795579403211671, 17235101634895315375, 153440975825762815938, -156894403296377741177371, -1454252568471818731501051, 2071137586315785548669378432

Offset: 0

Author

Ilya Gutkovskiy, Jun 13 2019

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..297
• Eric Weisstein's World of Mathematics, Complementary Bell Number

Crossrefs

Cf. A000587, A020557, A308647.

Programs

Maple

seq(BellB(2*n,-1),n=0..30); # Robert Israel, Jun 08 2020

Mathematica

Table[Exp[1] Sum[(-1)^k k^(2 n)/k!, {k, 0, Infinity}], {n, 0, 19}]
Table[BellB[2 n, -1], {n, 0, 19}]

Formula

a(n) = Sum_{k=0..2*n} (-1)^k*Stirling2(2*n,k).

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