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 A381056 #80 Apr 01 2025 03:28:14
%S A381056 1,16,4320,7680000,56672000000,1315328716800000,79725223359774720000,
%T A381056 11041460968683995136000000,3159164253667495772160000000000,
%U A381056 1725992749819407775039488000000000000,1690274868390850110509130354524160000000000,2816890048270042497343000411961733572198400000000
%N A381056 Product of row n of A329708.
%F A381056 a(n) = Product_{k=0..2*n} A329708(n,k).
%F A381056 a(n) = Product_{k=0..2*n} (Sum_{i=max(0,k-n)..min(k,n)} (i+1)*(k-i+1)).
%F A381056 a(n) == 0 (mod (n+1)^3).
%F A381056 a(n) = (n+1)*(n+2)*(n+3)*(1/6)*(Product_{k=1..n} k*(k+1)*(k+2)*((n+k+1)*(n+k+2)*(n+k+3)-2*k*(k+1)*(3*n+k+5))/36).
%F A381056 a(n) = binomial(n+3,3)*(Product_{k=1..n} binomial(k+2,3)*(binomial(k+n+3,3)-(k*(k+1)*(3*n+k+5))/3)).
%F A381056 a(n) = (Product_{k=0..n-1} Sum_{i=0..k} (i+1)*(k-i+1)) * (Product_{k=n..2*n} Sum_{i=k-n..n} (i+1)*(k-i+1)).
%F A381056 a(n) = (Product_{k=0..n-1} binomial(k+3,3))*(Product{k=n..2*n} binomial(k+3,3)-(2*n+4)*binomial(k+2-n)+(2*n+2)*binomial(k+1-n)).
%e A381056 Row n=2 of A329708 is {1, 4, 10, 12, 9} and the product of those is a(2) = 4320.
%o A381056 (Python)
%o A381056 from sympy import prod
%o A381056 def a(n):
%o A381056 p = ((n+1)*(n+2)*(n+3)) // 6
%o A381056 p *= prod(((k*(k+1)*(k+2))*((n+k+1)*(n+k+2)*(n+k+3)-2*k*(k+1)*(3*n+k+5)))//36 for k in range(1,n+1))
%o A381056 return p
%o A381056 print([a(n) for n in range(0, 14)])
%o A381056 (PARI) a(n) = vecprod(Vec(sum(k=0, n, (k+1)*x^k)^2)); \\ _Michel Marcus_, Feb 13 2025
%Y A381056 Cf. A000290, A000292, A000537, A005408, A007531, A087047, A329708.
%K A381056 nonn
%O A381056 0,2
%A A381056 _Darío Clavijo_, Feb 12 2025