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