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 A384364 #15 May 28 2025 04:33:12
%S A384364 1,1,1,1,3,1,1,21,9,1,1,219,657,27,1,1,3045,119241,22869,81,1,1,52923,
%T A384364 40365873,80850987,836001,243,1,1,1103781,21955523049,747786838869,
%U A384364 60579666801,31436181,729,1,1,26857659,17512689629457,14298291269335467,16117269494868801,48066954848379,1204022961,2187,1
%N A384364 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = Sum_{i=0..k*n} 3^i * Sum_{j=0..i} (-1)^j * binomial(i,j) * binomial(i-j,n)^k.
%F A384364 A(n,k) = (1/4) * Sum_{j>=0} (3/4)^j * binomial(j,n)^k.
%e A384364 Square array begins:
%e A384364 1, 1, 1, 1, 1, ...
%e A384364 1, 3, 21, 219, 3045, ...
%e A384364 1, 9, 657, 119241, 40365873, ...
%e A384364 1, 27, 22869, 80850987, 747786838869, ...
%e A384364 1, 81, 836001, 60579666801, 16117269494868801, ...
%o A384364 (PARI) a(n, k) = sum(i=0, k*n, 3^i*sum(j=0, i, (-1)^j*binomial(i, j)*binomial(i-j, n)^k));
%Y A384364 Columns k=0..2 give A000012, A000244, 3^n * A084768(n).
%Y A384364 Rows n=0..1 give A000012, A032033.
%Y A384364 Cf. A262809, A384362.
%K A384364 nonn,tabl
%O A384364 0,5
%A A384364 _Seiichi Manyama_, May 27 2025