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A176467 A symmetrical triangle:q=2;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=A060187(n,m)-c(n,q)/(c(m,q)*c(n-m,q))+1.

%I A176467 #4 Jun 02 2025 02:52:34
%S A176467 1,1,1,1,4,1,1,17,17,1,1,62,196,62,1,1,207,1528,1528,207,1,1,660,9893,
%T A176467 22154,9893,660,1,1,2053,57991,247913,247913,57991,2053,1,1,6298,
%U A176467 320818,2388134,4474228,2388134,320818,6298,1,1,19163,1712906,20919938
%N A176467 A symmetrical triangle:q=2;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=A060187(n,m)-c(n,q)/(c(m,q)*c(n-m,q))+1.
%C A176467 Row sums are:
%C A176467 {1, 2, 6, 36, 322, 3472, 43262, 615916, 9904730, 177511112, 3486135606,...}.
%F A176467 q=2;
%F A176467 c(n,q)=Product[1 - q^i, {i, 1, n}];
%F A176467 t(n,m,q)=A060187(n,m)-c(n,q)/(c(m,q)*c(n-m,q))+1
%e A176467 {1},
%e A176467 {1, 1},
%e A176467 {1, 4, 1},
%e A176467 {1, 17, 17, 1},
%e A176467 {1, 62, 196, 62, 1},
%e A176467 {1, 207, 1528, 1528, 207, 1},
%e A176467 {1, 660, 9893, 22154, 9893, 660, 1},
%e A176467 {1, 2053, 57991, 247913, 247913, 57991, 2053, 1},
%e A176467 {1, 6298, 320818, 2388134, 4474228, 2388134, 320818, 6298, 1},
%e A176467 {1, 19163, 1712906, 20919938, 66103548, 66103548, 20919938, 1712906, 19163, 1},
%e A176467 {1, 58016, 8941891, 171953190, 853179296, 1417870818, 853179296, 171953190, 8941891, 58016, 1}
%t A176467 (*A060187*);
%t A176467 p[x_, n_] = (1 - x)^(n + 1)*Sum[(2*k + 1)^n*x^k, {k, 0, Infinity}];
%t A176467 f[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];
%t A176467 c[n_, q_] = Product[1 - q^i, {i, 1, n}];
%t A176467 t[n_, m_, q_] := f[n, m] - c[n, q]/(c[m, q]*c[n - m, q]) + 1;
%t A176467 Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]
%Y A176467 Cf. A060187
%K A176467 nonn,tabl,uned
%O A176467 0,5
%A A176467 _Roger L. Bagula_, Apr 18 2010