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 A061693 #17 Apr 17 2022 14:11:28
%S A061693 0,4,27,172,1125,7591,52479,369580,2640465,19082629,139207959,
%T A061693 1023462199,7574172879,56369211679,421563478527,3166149812140,
%U A061693 23868662788809,180538738842217,1369635435497367,10418413517675797
%N A061693 Generalized Bell numbers.
%H A061693 J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/SIXDENIERS/bell.html">Extended Bell and Stirling Numbers From Hypergeometric Exponentiation</a>, J. Integer Seqs. Vol. 4 (2001), #01.1.4.
%F A061693 a(n) = A000172(n)/2-1. - _Vladeta Jovovic_, Apr 23 2003
%F A061693 Sum_{n>=1} a(n) * x^n / (n!)^3 = (1/2) * ( Sum_{n>=1} x^n / (n!)^3 )^2. - _Ilya Gutkovskiy_, Mar 04 2021
%t A061693 a[n_] := Sum[Binomial[n, k]^3, {k, 0, n}]/2 - 1;
%t A061693 a[n_] := n^2*HypergeometricPFQ[{1 - n, 1 - n, 1 - n}, {2, 2}, -1] - 1;
%t A061693 Table[a[n], {n, 1, 20}] (* _Peter Luschny_, Apr 17 2022 *)
%K A061693 nonn
%O A061693 1,2
%A A061693 _N. J. A. Sloane_, Jun 19 2001