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
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..297
- Eric Weisstein's World of Mathematics, Complementary Bell Number
Programs
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Maple
seq(BellB(2*n,-1),n=0..30); # Robert Israel, Jun 08 2020
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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).