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 A291973 #23 Jun 20 2024 08:35:42
%S A291973 1,1,11,365,25323,3068521,583027547,161601254725,62042488237755,
%T A291973 31728742163212641,20963751508027371691,17461136553331587079965,
%U A291973 17967906090023681913528523,22459900935806853610377326041,33617974358392980795259947648187,59515082206147526028817472280664565
%N A291973 a(n) = (3*n)! * [z^(3*n)] exp(exp(z)/3 + 2*exp(-z/2)*cos(z*sqrt(3)/2)/3 - 1).
%C A291973 Row sums of A291451.
%C A291973 The number of set partitions of {1,2,...,3n} where the size of every block is a multiple of 3. - _Per W. Alexandersson_, Jun 20 2024
%H A291973 Andrew Howroyd, <a href="/A291973/b291973.txt">Table of n, a(n) for n = 0..100</a>
%F A291973 a(0) = 1; a(n) = Sum_{k=1..n} binomial(3*n-1,3*k-1) * a(n-k). - _Ilya Gutkovskiy_, Jan 21 2020
%e A291973 For n=2, there are a(2)=11 partitions of {1,2,...,6} with every block size a multiple of 3: 123456, 123|456, 124|356, 125|346, 126|345, 134|256, 135|246, 136|245, 145|236, 146|235 and 156|234. - _Per W. Alexandersson_, Jun 20 2024
%p A291973 A291973 := proc(n) exp(exp(z)/3+2*exp(-z/2)*cos(z*sqrt(3)/2)/3-1):
%p A291973 (3*n)!*coeff(series(%, z, 3*(n+1)), z, 3*n) end:
%p A291973 seq(A291973(n), n=0..15);
%t A291973 P[m_, n_] := P[m, n] = If[n == 0, 1, Sum[Binomial[m*n, m*k]*P[m, n - k]*x, {k, 1, n}]];
%t A291973 a[n_] := Module[{cl = CoefficientList[P[3, n], x]}, Sum[cl[[k + 1]]/k!, {k, 0, n}]];
%t A291973 Table[a[n], {n, 0, 15}] (* _Jean-François Alcover_, Jul 23 2019, after _Peter Luschny_ in A291451 *)
%o A291973 (PARI) seq(n)={my(a=vector(n+1)); a[1]=1; for(n=1, n, a[1+n]=sum(k=1, n, binomial(3*n-1, 3*k-1) * a[1+n-k])); a} \\ _Andrew Howroyd_, Jan 21 2020
%Y A291973 Cf. A291451.
%K A291973 nonn
%O A291973 0,3
%A A291973 _Peter Luschny_, Sep 07 2017