This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A091552 #10 Aug 30 2025 02:43:15
%S A091552 1,308,154840,121284800,138146444800,216595133081600,
%T A091552 448169865375232000,1184352885735219200000,3894384547720687820800000,
%U A091552 15599967808704696966348800000,74806554280938737689393561600000,423166219648146647212581257216000000,2788777788711380327670376970321920000000
%N A091552 Second column (k=3) sequence of array A092077 ((8,2)-Stirling2) divided by 16.
%H A091552 Pawel Blasiak, Karol A. Penson, and Allan I. Solomon, <a href="https://doi.org/10.1016/S0375-9601(03)00194-4">The general boson normal ordering problem</a>, Physics Letters A, Vol. 309, No. 3-4 (2003), pp. 198-205; <a href="https://arxiv.org/abs/quant-ph/0402027">arXiv preprint</a>, arXiv:quant-ph/0402027, 2004.
%F A091552 E.g.f.: (hypergeom([1/3, 1/2], [], 36*x) - 3*hypergeom([1/6, 1/3], [], 36*x) + 2)/(3!*16).
%F A091552 a(n) = (2^n) * Product_{j=0..n-1} (3*j+1) * (-3*Product_{j=0..n-1} (6*j+1) + Product_{j=0..n-1} (6*j+3))/(3!*16), n>=2. From eq.12 of the Blasiak et al. reference with r=8, s=2, k=3.
%F A091552 a(n) = (2^(2*n-5)) * (3^(2*n-1)) * risefac(1/3, n) * (-3*risefac(1/6, n) + risefac(1/2, n)), n>=2, with risefac(x, n) = Pochhammer(x, n).
%F A091552 a(n) ~ sqrt(Pi) * 2^(2*n-4) * 3^(2*n-1) * n^(2*n-1/6) / (Gamma(1/3) * exp(2*n)). - _Amiram Eldar_, Aug 30 2025
%t A091552 a[n_] := 2^(2*n-5) * 3^(2*n-1) * Pochhammer[1/3, n] * (-3 * Pochhammer[1/6, n] + Pochhammer[1/2, n]); Array[a, 20, 2] (* _Amiram Eldar_, Aug 30 2025 *)
%Y A091552 Cf. A091551 (second column of (7, 2)-Stirling2 array).
%K A091552 nonn,easy,changed
%O A091552 2,2
%A A091552 _Wolfdieter Lang_, Feb 13 2004