A272230 E.g.f.: 2*exp(x)/(exp(2*x)+1+2*x).

1, -1, 3, -15, 93, -725, 6815, -74627, 933849, -13148361, 205690779, -3539545559, 66446203637, -1351309774685, 29595401433975, -694475294514315, 17382734374217265, -462283425487469585, 13017336622169166515, -386916316537712637215, 12105656546432789499405, -397693919494074869853285

Offset

0,3

Comments

Empirically, for odd n, n|a(n) and for even n, (n-1)|a(n).

Links

Robert Israel, Table of n, a(n) for n = 0..418

Formula

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

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

a(n) ~ n! * (-1)^n*sqrt(LambertW(exp(-1)))*2^(n+1) / (1+LambertW(exp(-1)))^(n+2). - Vaclav Kotesovec, May 03 2016

Maple

S:= series(2*exp(x)/(exp(2*x)+1+2*x), x, 31):
seq(coeff(S, x, j)*j!, j=0..30); # Robert Israel, May 24 2016

Mathematica

a[n_]:=Sum[Sum[Sum[Binomial[k, j]*Binomial[k + i, i]*Binomial[n, i]*((i!*(-1)^(i + j)*(2 j + 1)^(n - i))/(2^k)), {i, 0, n}], {j, 0, k}], {k, 0, n}]

Crossrefs

Cf. A000364, A122045.

Sequence in context: A060066 A206177 A366638 * A308457 A241711 A243245

Adjacent sequences: A272227 A272228 A272229 * A272231 A272232 A272233

Keyword

sign

Author

Christopher Ernst, Apr 22 2016

Status

approved