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 A368840 #13 May 26 2024 14:36:09
%S A368840 1,2,9,91,1821,63736,3569217,299814229,35977707481,5936321734366,
%T A368840 1305990781560521,373513363526309007,135958864323576478549,
%U A368840 61861283267227297739796,34642318629647286734285761,23556776668160154979314317481
%N A368840 a(n) = n! * (n+1)! * (n+2)! * Sum_{k=0..n} 1/(6^(n-k) * k! * (k+1)! * (k+2)!).
%H A368840 Harvey P. Dale, <a href="/A368840/b368840.txt">Table of n, a(n) for n = 0..203</a>
%F A368840 a(n) = binomial(n+2,3)*a(n-1) + 1.
%t A368840 nxt[{n_,a_}]:={n+1,a*Binomial[n+3,3]+1}; NestList[nxt,{0,1},20][[;;,2]] (* _Harvey P. Dale_, May 26 2024 *)
%o A368840 (PARI) a(n) = n!*(n+1)!*(n+2)!*sum(k=0, n, 1/(6^(n-k)*k!*(k+1)!*(k+2)!));
%Y A368840 Cf. A000522, A228230.
%Y A368840 Cf. A368839.
%K A368840 nonn,easy
%O A368840 0,2
%A A368840 _Seiichi Manyama_, Jan 07 2024