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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

Table of n, a(n) for n=1..34.

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

A142459

Sequence in context: A144948 A108335 A239474 * A143378 A131961 A010269

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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Last modified December 19 07:15 EST 2014. Contains 252178 sequences.