A371309 Expansion of e.g.f. Product_{k>=1} (1 + x^k/k!)^(k^2).

1, 1, 4, 21, 88, 645, 4386, 33061, 296808, 2674377, 26757190, 285294801, 3199971336, 38104015417, 476816609192, 6261875218215, 85736036949856, 1227373767823617, 18255004438680558, 281702101344334993, 4509097743074878200, 74606738071821274641, 1275212550939684334384

Offset: 0

Author

Ilya Gutkovskiy, Mar 24 2024

Keywords

• nonn

Comments

"EGJ" (unordered, element, labeled) transform of squares.

Links

• C. G. Bower, Transforms (2)

Crossrefs

Cf. A000290, A007837, A027998, A032315, A032316.

Programs

Mathematica

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