OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
E.g.f. for offset 1: (log((1-x)(1-2x))/(2x-3)+log((1-x)(1+x))/x)/3; a(n) = n!*sum{k=0..n, J(k)/binomial(n, k)}; a(n) = sum{k=0..n, k!*J(k)*(n-k)!}.
Recurrence: 3*(n+2)*(10*n^2 + 9*n - 15)*a(n) = 2*(n+1)*(40*n^3 + 71*n^2 - 90*n - 30)*a(n-1) - n^2*(10*n^3 + 9*n^2 - 116*n + 41)*a(n-2) - 2*(n-1)^2*n*(40*n^3 + 66*n^2 - 107*n - 24)*a(n-3) + 4*(n-2)^2*(n-1)^2*n*(10*n^2 + 29*n + 4)*a(n-4). - Vaclav Kotesovec, Sep 25 2013
a(n) ~ n!*2^n/3. - Vaclav Kotesovec, Sep 25 2013
MATHEMATICA
Table[Sum[k!*(2^k - (-1)^k)/3*(n - k)!, {k, 0, n}], {n, 0, 10}] (* Vaclav Kotesovec, Sep 25 2013 *)
Rest[CoefficientList[Series[(Log[(1-x)*(1-2*x)]/(2*x-3)+Log[(1-x)*(1+x)]/x)/3, {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Sep 25 2013 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 21 2005
STATUS
approved