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 A176639 A q-form method for the symmetrical triangle sequence was found based on A000384 hexagonal numbers: q=3;c(n,q)=Product[(q*(2*q - 1))^i, {i, 1, n}];t(n,m,q)=c(n,q)/(c(m,q)*c(n-m,q)- c(n,q)/(c(0,q)*c(n-0,q)+1 0
 1, 1, 1, 1, 15, 1, 1, 225, 225, 1, 1, 3375, 50625, 3375, 1, 1, 50625, 11390625, 11390625, 50625, 1, 1, 759375, 2562890625, 38443359375, 2562890625, 759375, 1, 1, 11390625, 576650390625, 129746337890625, 129746337890625, 576650390625, 11390625, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS q=2 is A158116. Row sums are: {1, 2, 17, 452, 57377, 22882502, 43570659377, 260645999343752, 7444455629492109377, 668007188161858153125002, 286189883115807009506818359377,...}. LINKS FORMULA q=3; c(n,q)=Product[(q*(2*q - 1))^i, {i, 1, n}]; t(n,m,q)=c(n,q)/(c(m,q)*c(n-m,q)- c(n,q)/(c(0,q)*c(n-0,q)+1 EXAMPLE {1}, {1, 1}, {1, 15, 1}, {1, 225, 225, 1}, {1, 3375, 50625, 3375, 1}, {1, 50625, 11390625, 11390625, 50625, 1}, {1, 759375, 2562890625, 38443359375, 2562890625, 759375, 1}, {1, 11390625, 576650390625, 129746337890625, 129746337890625, 576650390625, 11390625, 1}, {1, 170859375, 129746337890625, 437893890380859375, 6568408355712890625, 437893890380859375, 129746337890625, 170859375, 1}, {1, 2562890625, 29192926025390625, 1477891880035400390625, 332525673007965087890625, 332525673007965087890625, 1477891880035400390625, 29192926025390625, 2562890625, 1}, {1, 38443359375, 6568408355712890625, 4987885095119476318359375, 16834112196028232574462890625, 252511682940423488616943359375, 16834112196028232574462890625, 4987885095119476318359375, 6568408355712890625, 38443359375, 1} MATHEMATICA Clear[t, n, m, c, q]; c[n_, q_] = Product[(q*(2*q - 1))^i, {i, 1, n}]; t[n_, m_, q_] = c[n, q]/(c[m, q]*c[n - m, q]) - c[n, q]/(c[0, q]*c[n - 0, q]) + 1; Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}] CROSSREFS Cf. A000384, A158116 Sequence in context: A174187 A174693 A022178 * A015139 A040231 A040232 Adjacent sequences:  A176636 A176637 A176638 * A176640 A176641 A176642 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Apr 22 2010 STATUS approved

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Last modified June 2 14:04 EDT 2020. Contains 334781 sequences. (Running on oeis4.)