A371481 Expansion of e.g.f. Product_{k>=1} (1 + x^k/k!)^(k*(k+1)/2).

1, 1, 3, 15, 52, 335, 2031, 12880, 102614, 802443, 6956995, 64721756, 633754320, 6551212057, 71375943289, 820250162880, 9747543483676, 121775559807881, 1580353806494781, 21246545374234378, 296590230821338520, 4280692741624646151, 63852747607056438283

Offset: 0

Author

Ilya Gutkovskiy, Mar 25 2024

Keywords

• nonn

Comments

"EGJ" (unordered, element, labeled) transform of triangular numbers.

Links

• C. G. Bower, Transforms (2)

Crossrefs

Cf. A000217, A007837, A028377, A032315, A032316, A371309.

Programs

Mathematica

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