[seqfan] possible genfunc for A137341

[Joerg Arndt]

http://www.research.att.com/~njas/sequences/A137341

appears to be reproduced by (pari/gp):

? default(seriesprecision,16);
? Vec(serlaplace(serlaplace(exp(sum(k=1,16,1*x^k/(k!))))))
[1, 1, 4, 30, 360, 6240, 146160, 4420080, 166924800, 7673823360,
 420850080000, 27086342976000, 2018319704755200, 172142484203289600,
 16642276683198566400, 1808459441303074560000,
 219273812138054209536000]

If anyone sees why this would be true, please
add as a comment to the seq!

How do we call such a generating function?
 EEGF ??