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 A143188 A symmetrical triangle sequence with low, even center: t(n,m)=If[(n - m)*m == 0, 1, If[m <= Floor[n/2] && Mod[m, 2] == 1, 2*m, If[m <= Floor[n/2] && Mod[m, 2] == 0, m, If[m > Floor[n/2] && Mod[n - m, 2] == 1, 2*(n - m), If[m > Floor[n/2] && Mod[n - m, 2] == 0, (n - m), n - m]]]]]*Binomial[n, m]. 0
 1, 1, 1, 1, 4, 1, 1, 6, 6, 1, 1, 8, 12, 8, 1, 1, 10, 20, 20, 10, 1, 1, 12, 30, 120, 30, 12, 1, 1, 14, 42, 210, 210, 42, 14, 1, 1, 16, 56, 336, 280, 336, 56, 16, 1, 1, 18, 72, 504, 504, 504, 504, 72, 18, 1, 1, 20, 90, 720, 840, 2520, 840, 720, 90, 20, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums are: {1, 2, 6, 14, 30, 62, 206, 534, 1098, 2198, 5862}. LINKS FORMULA t(n,m)=If[(n - m)*m == 0, 1, If[m <= Floor[n/2] && Mod[m, 2] == 1, 2*m, If[m <= Floor[n/2] && Mod[m, 2] == 0, m, If[m > Floor[n/2] && Mod[n - m, 2] == 1, 2*(n - m), If[m > Floor[n/2] && Mod[n - m, 2] == 0, (n - m), n - m]]]]]*Binomial[n, m]. EXAMPLE {1}, {1, 1}, {1, 4, 1}, {1, 6, 6, 1}, {1, 8, 12, 8, 1}, {1, 10, 20, 20, 10, 1}, {1, 12, 30, 120, 30, 12, 1}, {1, 14, 42, 210, 210, 42, 14, 1}, {1, 16, 56, 336, 280, 336, 56, 16, 1}, {1, 18, 72, 504, 504, 504, 504, 72, 18, 1}, {1, 20, 90, 720, 840, 2520, 840, 720, 90, 20, 1} MATHEMATICA Clear[t, n, m]; t[n_, m_] = If[(n - m)*m == 0, 1, If[m <= Floor[n/2] && Mod[m, 2] == 1, 2*m, If[m <= Floor[n/2] && Mod[m, 2] == 0, m, If[m > Floor[n/2] && Mod[n - m, 2] == 1, 2*(n - m), If[m > Floor[n/2] && Mod[n - m, 2] == 0, (n - m), n - m]]]]]*Binomial[n, m]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A159040 A132046 A141540 * A102413 A144480 A144463 Adjacent sequences:  A143185 A143186 A143187 * A143189 A143190 A143191 KEYWORD nonn,uned AUTHOR Roger L. Bagula and Gary W. Adamson, Oct 17 2008 STATUS approved

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Last modified April 5 20:22 EDT 2020. Contains 333260 sequences. (Running on oeis4.)