A330209 Nonzero coefficients of the polynomials (x + d/dx)^n x^2, in row-major order.
1, 2, 1, 2, 5, 1, 12, 9, 1, 12, 39, 14, 1, 90, 95, 20, 1, 90, 375, 195, 27, 1, 840, 1155, 357, 35, 1, 840, 4305, 2940, 602, 44, 1, 9450, 16065, 6552, 954, 54, 1, 9450, 57645, 48825, 13230, 1440, 65, 1, 124740, 252945, 128205, 24750, 2090, 77, 1, 124740, 883575, 893970, 301455, 43560, 2937, 90, 1
Offset: 0
Examples
x^2 ; 2x + x^3; 2 + 5x^2 + x^4; 12x + 9x^3 + x^5.
Links
- Robert S. Maier, Boson Operator Ordering Identities from Generalized Stirling and Eulerian Numbers, arXiv:2308.10332 [math.CO], 2023. See p. 19.
Crossrefs
Cf. A096713.
Comments