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.

A364072 Triangle read by rows: T(n, k) = Sum_{d=0..n-k} binomial(n, d)*StirlingS2(n-d, k)*63^(n-d-k), with 0 <= k <= n.

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%I A364072 #6 Jul 06 2023 21:13:54
%S A364072 1,1,1,1,65,1,1,4161,192,1,1,266305,28545,382,1,1,17043521,3891520,
%T A364072 101125,635,1,1,1090785345,511266561,23105270,261780,951,1,1,
%U A364072 69810262081,66021638592,4901267861,89335610,562296,1330,1,1,4467856773185,8454558363265,997262532182,27503177191,267021146,1066366,1772,1
%N A364072 Triangle read by rows: T(n, k) = Sum_{d=0..n-k} binomial(n, d)*StirlingS2(n-d, k)*63^(n-d-k), with 0 <= k <= n.
%C A364072 T(n, k) is the number of 64-subgroups of R^n which have dimension k, where R^n is a near-vector space over a proper nearfield R.
%H A364072 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. 7-9.
%e A364072 The triangle begins:
%e A364072   1;
%e A364072   1,          1;
%e A364072   1,         65,         1;
%e A364072   1,       4161,       192,        1;
%e A364072   1,     266305,     28545,      382,      1;
%e A364072   1,   17043521,   3891520,   101125,    635,   1;
%e A364072   1, 1090785345, 511266561, 23105270, 261780, 951, 1;
%e A364072   ...
%t A364072 T[n_,k_]:=Sum[Binomial[n,d]StirlingS2[n-d,k]63^(n-d-k),{d,0,n-k}]; Table[T[n,k],{n,0,8},{k,0,n}]//Flatten
%Y A364072 Cf. A000012 (k=0), A133853 (k=1), A364069 (row sums), A364071, A364073.
%K A364072 nonn,tabl
%O A364072 0,5
%A A364072 _Stefano Spezia_, Jul 04 2023