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 A146765 Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 1)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]. 0
 1, 1, 1, 1, 10, 1, 1, 27, 27, 1, 1, 68, 102, 68, 1, 1, 165, 330, 330, 165, 1, 1, 390, 975, 1300, 975, 390, 1, 1, 903, 2709, 4515, 4515, 2709, 903, 1, 1, 2056, 7196, 14392, 17990, 14392, 7196, 2056, 1, 1, 4617, 18468, 43092, 64638, 64638, 43092, 18468, 4617, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are:{1, 2, 12, 56, 240, 992, 4032, 16256, 65280, 261632, 1047552}. LINKS EXAMPLE Triangle begins: {1}, {1, 1}, {1, 10, 1}, {1, 27, 27, 1}, {1, 68, 102, 68, 1}, {1, 165, 330, 330, 165, 1}, {1, 390, 975, 1300, 975, 390, 1}, {1, 903, 2709, 4515, 4515, 2709, 903, 1}, {1, 2056, 7196, 14392, 17990, 14392, 7196, 2056, 1}, {1, 4617, 18468, 43092, 64638, 64638, 43092, 18468, 4617, 1}, {1, 10250, 46125, 123000, 215250, 258300, 215250, 123000, 46125, 10250, 1} MATHEMATICA p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n - 1)*Sum[Binomial[n, 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: A113280 A159041 A154979 * A190152 A154984 A173047 Adjacent sequences:  A146762 A146763 A146764 * A146766 A146767 A146768 KEYWORD nonn,tabl,less AUTHOR Roger L. Bagula, Nov 02 2008 STATUS approved

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Last modified December 5 20:39 EST 2021. Contains 349558 sequences. (Running on oeis4.)