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 A361042 #10 Mar 28 2024 21:56:46
%S A361042 1,1,2,1,3,4,1,4,7,10,1,5,11,17,34,1,6,16,28,51,154,1,7,22,44,79,205,
%T A361042 874,1,8,29,66,123,284,1079,5914,1,9,37,95,189,407,1363,6993,46234,1,
%U A361042 10,46,132,284,596,1770,8356,53227,409114,1,11,56,178,416,880,2366,10126,61583,462341,4037914
%N A361042 Triangle read by rows: T(n, k) = Sum_{j=0..n} j! * binomial(n - j, n - k).
%e A361042 Triangle T(n, k) starts:
%e A361042 [0] 1;
%e A361042 [1] 1, 2;
%e A361042 [2] 1, 3, 4;
%e A361042 [3] 1, 4, 7, 10;
%e A361042 [4] 1, 5, 11, 17, 34;
%e A361042 [5] 1, 6, 16, 28, 51, 154;
%e A361042 [6] 1, 7, 22, 44, 79, 205, 874;
%e A361042 [7] 1, 8, 29, 66, 123, 284, 1079, 5914;
%e A361042 [8] 1, 9, 37, 95, 189, 407, 1363, 6993, 46234;
%e A361042 [9] 1, 10, 46, 132, 284, 596, 1770, 8356, 53227, 409114.
%Y A361042 Cf. A003422 (main diagonal), A014144 (subdiagonal), A152689, A233449 (row sums), A133942 (alternating row sums), A293468 (central row).
%K A361042 nonn,tabl
%O A361042 0,3
%A A361042 _Peter Luschny_, Mar 13 2023