OFFSET
0,2
FORMULA
Recurrence: (n+2)*(n+4)*a(n) = 6*(n^2 + 3*n + 1)*a(n-1) + 4*(n-1)*(n+1)*a(n-2) - 24*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Feb 18 2015
a(n) ~ 9 * 6^(n+1) / (Pi * n^3). - Vaclav Kotesovec, Feb 18 2015
E.g.f.: exp(2*x)*BesselI(1,2*x)^2/x^2. - Ilya Gutkovskiy, Sep 21 2017
MATHEMATICA
Array[Cat, 21, 0]; For[i = 0, i < 21, ++i, Cat[i] = (1/(i + 1))*Binomial[2*i, i]]; Array[Mot, 21, 0]; For[i = 0, i < 21, ++i, Mot[i] = Sum[Binomial[i, 2*j]*Cat[j], {j, 0, Floor[i/2]}]]; Table[Sum[Binomial[n, j]*Mot[j]*Mot[n - j], {j, 0, n}], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric S. Egge, Oct 22 2008
EXTENSIONS
More terms from Alois P. Heinz, Feb 18 2015
STATUS
approved