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 A091551 #11 Aug 30 2025 02:43:19
%S A091551 1,228,83232,46854720,38109367296,42479241412608,62290218157719552,
%T A091551 116373513947009679360,270010358636135897235456,
%U A091551 762020881523854021734432768,2571195906705444158241905836032,10223478528521152233103572672184320,47315411140234001777600560898513043456
%N A091551 Second column (k=3) sequence of array ((7,2)-Stirling2) divided by 14.
%H A091551 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 A091551 a(n) = Product_{j=0..n-1} (5*j+2) * (-3*Product_{j=0..n-1} (5*j+1) + Product_{j=0..n-1} (5*j+3)/(3!*14), n>=2. From eq.12 of the Blasiak et al. reference with r=7, s=2, k=3.
%F A091551 a(n) = (5^(2*n))*risefac(2/5, n) * (-3*risefac(1/5, n) + risefac(3/5, n))/(3!*14), n>=2, with risefac(x, n) = Pochhammer(x, n).
%F A091551 E.g.f.: (hypergeom([2/5, 3/5], [], 25*x) - 3*hypergeom([1/5, 2/5], [], 25*x) + 2)/(3!*14).
%F A091551 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 A091551 a[n_] := 5^(2*n) * Pochhammer[2/5, n] * (-3 * Pochhammer[1/5, n] + Pochhammer[3/5, n])/(3!*14); Array[a, 20, 2] (* _Amiram Eldar_, Aug 30 2025 *)
%Y A091551 Cf. A091550 (second column of (6, 2)-Stirling2 array), A091552 (second column of (8, 2)-Stirling2 array).
%K A091551 nonn,easy,changed
%O A091551 2,2
%A A091551 _Wolfdieter Lang_, Feb 13 2004
%E A091551 Offset corrected by _Amiram Eldar_, Aug 30 2025