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 A061690 #17 Mar 04 2021 16:21:13
%S A061690 0,0,6,72,650,5400,43757,353192,2862330,23352300,191891117,1587587760,
%T A061690 13215894133,110619113423,930376519256,7858437064232,66627124896218,
%U A061690 566791391339532,4836144006188165,41375938305568772,354859541163656045
%N A061690 Generalized Stirling numbers.
%H A061690 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 A061690 a(n) = s(n, k) = Sum_{pi} n!/(k(1)! * 1!^k(1) * k(2)! * 2!^k(2) * ... * k(n)! * n!^k(n)) * (n!/(1!^k(1) * 2!^k(2) * ... * n!^k(n)))^L, where pi runs through all partitions k(1) +2 * k(2)+...+n * k(n) = n such that k = k(1)+k(2)+...+k(n), with k = 3 and L = 1.
%F A061690 Sum_{n>=1} a(n) * x^n / (n!)^2 = (BesselI(0,2*sqrt(x)) - 1)^3 / 6. - _Ilya Gutkovskiy_, Mar 04 2021
%o A061690 (PARI) a(n) = {n!^2*polcoef((besseli(0, 2*x + O(x^(2*n+1))) - 1)^3, 2*n)/6} \\ _Andrew Howroyd_, Mar 04 2021
%Y A061690 Third column of A061691.
%K A061690 nonn
%O A061690 1,3
%A A061690 _N. J. A. Sloane_, Jun 18 2001
%E A061690 Formula and more terms from _Vladeta Jovovic_, Dec 09 2001