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 A358112 #15 Nov 13 2022 14:32:57
%S A358112 1,5,1,47,42,1,641,1659,219,1,11389,72572,28470,968,1,248749,3610485,
%T A358112 3263402,357746,4017,1,6439075,204023334,371188155,95559940,3853617,
%U A358112 16278,1,192621953,12989570167,43844432805,22448025251,2216662051,38270373,65399,1
%N A358112 Table read by rows. A statistic of permutations of the multiset {1,1,2,2,...,n,n}.
%C A358112 Table 1, page 12 in Maazouz and Pitman (note a typo in T(2, 0)).
%H A358112 Yassine El Maazouz and Jim Pitman, <a href="https://doi.org/10.48550/arxiv.2210.02027">The Bernoulli clock: probabilistic and combinatorial interpretations of the Bernoulli polynomials by circular convolution</a>, arXiv:2210.02027 [math.PR], Oct. 2022.
%F A358112 T(n, k) = P(n, k+1) - P(n, k), where P(n, x) = (2*n)!*Sum_{k=0..n} Sum_{j=0..n-k} binomial(n, k)*binomial(n-k, j)*(-1)^(n-k-j)*max(x - k, 0)^(2*n - j)/(2*n - j)!.
%e A358112 [n\d] 0 1 2 3 4 5 6
%e A358112 -----------------------------------------------------------------------------
%e A358112 [1] 1;
%e A358112 [2] 5, 1;
%e A358112 [3] 47, 42, 1;
%e A358112 [4] 641, 1659, 219, 1;
%e A358112 [5] 11389, 72572, 28470, 968, 1;
%e A358112 [6] 248749, 3610485, 3263402, 357746, 4017, 1;
%e A358112 [7] 6439075, 204023334, 371188155, 95559940, 3853617, 16278, 1
%e A358112 [8] 192621953, 12989570167, 43844432805, 22448025251, 2216662051, 38270373,
%e A358112 65399, 1
%p A358112 P := (n, x) -> (2*n)!*add(add(binomial(n, k)*binomial(n-k, j)*
%p A358112 (-1)^(n-k-j)*max(x - k, 0)^(2*n - j)/(2*n - j)!, j = 0..n-k), k = 0..n):
%p A358112 Trow := n -> seq(P(n, k+1) - P(n, k), k = 0..n-1):
%p A358112 seq(print(Trow(n)), n = 1..8);
%Y A358112 Cf. A006902 (row 0), A000680 (row sums).
%K A358112 nonn,tabl
%O A358112 1,2
%A A358112 _Peter Luschny_, Oct 30 2022