A255432 E.g.f. sqrt(1-t^2)*exp(t*(1+arctanh(t))).

1, 1, 2, 4, 12, 36, 160, 680, 4368, 24976, 219616, 1599104, 18145600, 160805568, 2245960704, 23437238656, 389201754368, 4669754525952, 89893314615808, 1218303508421632, 26673872401980416, 402798557886395392, 9883555312758398976

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = a(n-1)+sum(k=1..n/2, (n-1)!/(n-2*k)!*(1/(2*k-1))*a(n-2*k)), a(0)=1.

a(n) ~ (n-2)! * (exp(1) + (-1)^n*exp(-1)). - Vaclav Kotesovec, Feb 24 2015

Mathematica

CoefficientList[Series[Sqrt[1-x^2]*E^(x*(1+Log[(1+x)/(1-x)]/2)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 24 2015 *)

Prog

(Maxima)
a(n):=if n=0 then 1 else a(n-1)+sum((n-1)!/(n-2*k)!*(1/(2*k-1))*a(n-2*k), k, 1, n/2);
(PARI) default(seriesprecision, 50); Vec(serlaplace(sqrt(1-t^2)*exp(t*(1+atanh(t))) + O(t^50)))

Crossrefs

Sequence in context: A349282 A276230 A003701 * A275539 A356062 A193049

Adjacent sequences: A255429 A255430 A255431 * A255433 A255434 A255435

Keyword

nonn

Author

Vladimir Kruchinin, Feb 23 2015

Status

approved