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 A155917 A difference triangle of Pascal-Sierpinski 5th level and the Pascal second derivative: a(n,k)= (4*n - 4*k + 1)a(n - 1, k - 1) + (4*k - 3)a(n - 1, k); p(x,n)=(Sum[10*n*(n - 1)*a(n, k)*x^(k - 1) - D[(x + 1)^(n + 2), {x, 2}]/(x + 1), {k, n}])/2 0
 -3, -2, -2, 0, 240, 0, 3360, 3360, -5, 30380, 105570, 30380, -5, -18, 232710, 2032620, 2032620, 232710, -18, -42, 1637748, 31186890, 74043480, 31186890, 1637748, -42, -80, 10932880, 420179760, 1990483600, 1990483600, 420179760, 10932880, -80 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row sums are: LINKS FORMULA a(n,k)= (4*n - 4*k + 1)a(n - 1, k - 1) + (4*k - 3)a(n - 1, k); p(x,n)=(Sum[10*n*(n - 1)*a(n, k)*x^(k - 1) - D[(x + 1)^(n + 2), {x, 2}]/(x + 1), {k, n}])/2; t(n,m)=coefficients(p(x,n)). EXAMPLE {-3}, {-2, -2}, {0, 240}, {0, 3360, 3360}, {-5, 30380, 105570, 30380, -5}, {-18, 232710, 2032620, 2032620, 232710, -18}, {-42, 1637748, 31186890, 74043480, 31186890, 1637748, -42}, {-80, 10932880, 420179760, 1990483600, 1990483600, 420179760, 10932880, -80}, {-135, 70305480, 5213648700, 44614752120, 87013084950, 44614752120, 5213648700, 70305480, -135}, {-210, 439442910, 61202397240, 887917071960, 3020166679140, 3020166679140, 887917071960, 61202397240, 439442910, -210} MATHEMATICA A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := (4*n - 4*k + 1)A[n - 1, k - 1] + (4*k - 3)A[n - 1, k]; a = Table[ExpandAll[(Sum[10*n*(n - 1)*A[n, k]*x^(k - 1) - D[(x + 1)^(n + 2), {x, 2}]/(x + 1), {k, n}])/2], {n, 10}]; Table[CoefficientList[ExpandAll[a[[n]]], x], {n, 1, Length[a]}]; Flatten[%] CROSSREFS Sequence in context: A144948 A108335 A239474 * A287823 A143378 A131961 Adjacent sequences:  A155914 A155915 A155916 * A155918 A155919 A155920 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Jan 30 2009 STATUS approved

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