OFFSET
0,2
LINKS
Nachum Dershowitz, Touchard’s Drunkard, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5.
FORMULA
Recurrence: (n+2)*(n+3)*(8*n+7)*a(n) = 3*(8*n^3 + 39*n^2 + 51*n + 22)*a(n-1) + (n-1)*(104*n^2 + 155*n - 30)*a(n-2) - 15*(n-2)*(n-1)*(8*n+15)*a(n-3). - Vaclav Kotesovec, Feb 18 2015
a(n) ~ 5^(n+2) / (2*Pi*n^2). - Vaclav Kotesovec, Feb 18 2015
MATHEMATICA
Table[Sum[ Binomial[n, j]*Binomial[n - j, Floor[(n - j)/2]]* Sum[Binomial[j, 2*i]*Binomial[2*i, i]/(i + 1), {i, 0, Floor[j/2]}], {j, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric S. Egge, Oct 21 2008
EXTENSIONS
More terms from Vaclav Kotesovec, Feb 18 2015
STATUS
approved