OFFSET
0,5
COMMENTS
LINKS
Peter Luschny, The lost Catalan numbers.
FORMULA
egf(x,y) = x*y*exp(x)*BesselI(0,2*x*y).
EXAMPLE
0
0, 1
0, 2, 0
0, 3, 0, 6
0, 4, 0, 24, 0
0, 5, 0, 60, 0, 30
0, 6, 0, 120, 0, 180, 0
0, 7, 0, 210, 0, 630, 0, 140
0
q
2 q
3 q + 6 q^3
4 q + 24 q^3
5 q + 60 q^3 + 30 q^5
6 q + 120 q^3 + 180 q^5
7 q + 210 q^3 + 630 q^5 + 140 q^7
MAPLE
MATHEMATICA
sf[n_] := n!/Quotient[n, 2]!^2;
row[n_] := Sum[Binomial[n, j] sf[j] q^j Mod[j, 2], {j, 0, n}] // CoefficientList[#, q]& // PadRight[#, n+1]&;
Table[row[n], {n, 0, 12}] (* Jean-François Alcover, Jun 26 2019 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Aug 29 2011
STATUS
approved