1 | initial version |

This is not a solution but only a very awkward attempt which illustrates what is missing (coefficient_list is home-brewed).

```
egf = 1 + sqrt(t)*exp((1+t)*x)*bessel_I(1,2*sqrt(t)*x)
tay = integral(taylor(egf, x, 0, 6),x)
r = coefficient_list(tay, x, true)
red = lambda i,o: o/i if i>0 else o
P = [red(ind, obj) for ind, obj in enumerate(r[1::])]
for narayana_poly in P:
print coefficient_list(narayana_poly, t)
[1]
[0, 1]
[0, 1, 1]
[0, 1, 3, 1]
[0, 1, 6, 6, 1]
[0, 1, 10, 20, 10, 1]
[0, 1, 15, 50, 50, 15, 1]
```

I suspect Sage will not get many friends at the OEIS if it cannot cope with such elementary maneuvers with generating functions.

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.