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 A384362 #18 May 28 2025 04:33:21
%S A384362 1,1,1,1,2,1,1,10,4,1,1,74,148,8,1,1,730,13540,2440,16,1,1,9002,
%T A384362 2308756,3087368,42256,32,1,1,133210,632363044,10208479240,778026256,
%U A384362 752800,64,1,1,2299754,253970683348,69754997963528,52520969994256,207633589664,13660480,128,1
%N A384362 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = Sum_{i=0..k*n} 2^i * Sum_{j=0..i} (-1)^j * binomial(i,j) * binomial(i-j,n)^k.
%F A384362 A(n,k) = (1/3) * Sum_{j>=0} (2/3)^j * binomial(j,n)^k.
%e A384362 Square array begins:
%e A384362 1, 1, 1, 1, 1, ...
%e A384362 1, 2, 10, 74, 730, ...
%e A384362 1, 4, 148, 13540, 2308756, ...
%e A384362 1, 8, 2440, 3087368, 10208479240, ...
%e A384362 1, 16, 42256, 778026256, 52520969994256, ...
%o A384362 (PARI) a(n, k) = sum(i=0, k*n, 2^i*sum(j=0, i, (-1)^j*binomial(i, j)*binomial(i-j, n)^k));
%Y A384362 Columns k=0..2 give A000012, A000079, A098270.
%Y A384362 Rows n=0..1 give A000012, A004123(k+1).
%Y A384362 Cf. A262809, A384364.
%K A384362 nonn,tabl
%O A384362 0,5
%A A384362 _Seiichi Manyama_, May 27 2025