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 A146955 A functionally symmetric Polynomial as a triangle of coefficients: p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 4)*Sum[(2^m + 2*m )*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]. 0
 1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 22, 22, 22, 1, 1, 61, 54, 54, 61, 1, 1, 190, 143, 132, 143, 190, 1, 1, 647, 421, 339, 339, 421, 647, 1, 1, 2344, 1372, 952, 838, 952, 1372, 2344, 1, 1, 8841, 4836, 2964, 2238, 2238, 2964, 4836, 8841, 1, 1, 34186, 17965, 10104, 6610 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are:{1, 2, 6, 20, 68, 232, 800, 2816, 10176, 37760, 143360}. LINKS FORMULA p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 4)*Sum[(2^m + 2*m )*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; t(n,m)=coefficients(p(x,n)). Conjecture: row sums are 2^n*(2^n+6-n+n^2)/8 for n>0. [From R. J. Mathar, Nov 30 2008] EXAMPLE {1}, {1, 1}, {1, 4, 1}, {1, 9, 9, 1}, {1, 22, 22, 22, 1}, {1, 61, 54, 54, 61, 1}, {1, 190, 143, 132, 143, 190, 1}, {1, 647, 421, 339, 339, 421, 647, 1}, {1, 2344, 1372, 952, 838, 952, 1372, 2344, 1}, {1, 8841, 4836, 2964, 2238, 2238, 2964, 4836, 8841, 1}, {1, 34186, 17965, 10104, 6610, 5628, 6610, 10104, 17965, 34186, 1} MATHEMATICA Clear[p, x, n]; p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n - 4)*Sum[(2^m + 2*m )*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A157192 A154982 A146767 * A155451 A220681 A189280 Adjacent sequences:  A146952 A146953 A146954 * A146956 A146957 A146958 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Nov 03 2008 STATUS approved

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)