cp's OEIS Frontend

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.

A364071 Triangle read by rows: T(n, k) = Sum_{d=0..n-k} binomial(n, d)*StirlingS2(n-d, k)*8^(n-d-k), with 0 <= k <= n.

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%I A364071 #6 Jul 06 2023 21:13:38
%S A364071 1,1,1,1,10,1,1,91,27,1,1,820,550,52,1,1,7381,10170,1850,85,1,1,66430,
%T A364071 180271,56420,4655,126,1,1,597871,3131037,1590771,210035,9821,175,1,1,
%U A364071 5380840,53825500,42900312,8521926,612696,18396,232,1,1,48427561,920414340,1126333300,324123870,33642462,1514100,31620,297,1
%N A364071 Triangle read by rows: T(n, k) = Sum_{d=0..n-k} binomial(n, d)*StirlingS2(n-d, k)*8^(n-d-k), with 0 <= k <= n.
%C A364071 T(n, k) is the number of 8-subgroups of R^n which have dimension k, where R^n is a near-vector space over a proper nearfield R.
%H A364071 Prudence Djagba and Jan Hązła, <a href="https://arxiv.org/abs/2306.16421">Combinatorics of subgroups of Beidleman near-vector spaces</a>, arXiv:2306.16421 [math.RA], 2023. See pp. 7-8.
%e A364071 The triangle begins:
%e A364071   1;
%e A364071   1,      1;
%e A364071   1,     10,       1;
%e A364071   1,     91,      27,      1;
%e A364071   1,    820,     550,     52,       1;
%e A364071   1,   7381,   10170,   1850,      85,    1;
%e A364071   1,  66430,  180271,  56420,    4655,  126,   1;
%e A364071   1, 597871, 3131037, 1590771, 210035, 9821, 175, 1;
%e A364071   ...
%t A364071 T[n_,k_]:=Sum[Binomial[n,d]StirlingS2[n-d,k]8^(n-d-k),{d,0,n-k}]; Table[T[n,k],{n,0,9},{k,0,n}]//Flatten
%Y A364071 Cf. A000012 (k=0), A002452 (k=1), A003580 (row sums), A364072, A364073.
%K A364071 nonn,tabl
%O A364071 0,5
%A A364071 _Stefano Spezia_, Jul 04 2023