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A376335 Irregular triangle read by rows: T(n,k) = A008949(n-1,k) if 0 <= k <= n - 2 otherwise A008949(n-1,2*n-4-k) if n - 2 <= k <= 2*n - 4.

%I A376335 #6 Sep 21 2024 02:23:16
%S A376335 1,1,3,1,1,4,7,4,1,1,5,11,15,11,5,1,1,6,16,26,31,26,16,6,1,1,7,22,42,
%T A376335 57,63,57,42,22,7,1,1,8,29,64,99,120,127,120,99,64,29,8,1,1,9,37,93,
%U A376335 163,219,247,255,247,219,163,93,37,9,1,1,10,46,130,256,382,466,502,511,502,466,382,256,130,46,10,1
%N A376335 Irregular triangle read by rows: T(n,k) = A008949(n-1,k) if 0 <= k <= n - 2 otherwise A008949(n-1,2*n-4-k) if n - 2 <= k <= 2*n - 4.
%H A376335 Nsibiet E. Udo, Praise Adeyemo, Balazs Szendroi, and Stavros Argyrios Papadakis, <a href="https://arxiv.org/abs/2409.10278">Ideals, representations and a symmetrised Bernoulli triangle</a>, arXiv:2409.10278 [math.AC], 2024. See p. 2.
%F A376335 Sum_{k=0..2*n-4} T(n,k) = A000337(n-1). [Udo et al.]
%e A376335 The triangle begins as:
%e A376335   1;
%e A376335   1, 3,  1;
%e A376335   1, 4,  7,  4,  1;
%e A376335   1, 5, 11, 15, 11,  5,  1;
%e A376335   1, 6, 16, 26, 31, 26, 16,  6,  1;
%e A376335   1, 7, 22, 42, 57, 63, 57, 42, 22, 7, 1;
%e A376335   ...
%t A376335 b[n_,k_]:=Sum[Binomial[n,j],{j,0,k}]; T[n_,k_]:=If[0<=k<=n-2,b[n-1,k],b[n-1,2n-4-k]]; Table[T[n,k],{n,2,10},{k,0,2n-4}]//Flatten
%Y A376335 Cf. A000337, A008949.
%K A376335 nonn,easy,tabf
%O A376335 2,3
%A A376335 _Stefano Spezia_, Sep 20 2024