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%I #16 Aug 23 2023 12:22:37
%S 1,2,1,2,5,1,12,9,1,12,39,14,1,90,95,20,1,90,375,195,27,1,840,1155,
%T 357,35,1,840,4305,2940,602,44,1,9450,16065,6552,954,54,1,9450,57645,
%U 48825,13230,1440,65,1,124740,252945,128205,24750,2090,77,1,124740,883575,893970,301455,43560,2937,90,1
%N Nonzero coefficients of the polynomials (x + d/dx)^n x^2, in row-major order.
%C The similar-looking polynomials (x-d/dx)^n * 1 are the probabilist's Hermite polynomials, A096713.
%H Robert S. Maier, <a href="https://arxiv.org/abs/2308.10332">Boson Operator Ordering Identities from Generalized Stirling and Eulerian Numbers</a>, arXiv:2308.10332 [math.CO], 2023. See p. 19.
%e x^2 ; 2x + x^3; 2 + 5x^2 + x^4; 12x + 9x^3 + x^5.
%Y Cf. A096713.
%K nonn,tabf
%O 0,2
%A _Chris Jones_, Dec 05 2019