A371482 - OEIS

A371482

Expansion of e.g.f. Product_{k>=1} (1 + x^k/k!)^(2^k).

%I #5 Mar 26 2024 11:14:25

%S 1,2,6,32,164,1032,7728,59376,522600,4946768,49680656,540031296,

%T 6195155744,75183755584,961596510272,12909563309952,181305865742240,

%U 2657525771641664,40594443765953472,643987597483557888,10601112599585001984,180727870834447607808,3185418524574895953152

%N Expansion of e.g.f. Product_{k>=1} (1 + x^k/k!)^(2^k).

%C "EGJ" (unordered, element, labeled) transform of powers of 2.

%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>

%t nmax = 22; CoefficientList[Series[Product[(1 + x^k/k!)^(2^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

%Y Cf. A000079, A007837, A032315, A032316, A102866, A199163.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Mar 25 2024