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A143185 A designed symmetrical triangle sequence: t(n,m)=If[m*(n - m) == 0, 1, (1 + Abs[(1 + n - m) - (1 + m)])*Binomial[n, m]]. 0
1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 6, 12, 1, 1, 20, 20, 20, 20, 1, 1, 30, 45, 20, 45, 30, 1, 1, 42, 84, 70, 70, 84, 42, 1, 1, 56, 140, 168, 70, 168, 140, 56, 1, 1, 72, 216, 336, 252, 252, 336, 216, 72, 1, 1, 90, 315, 600, 630, 252, 630, 600, 315, 90, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are:

{1, 3, 13, 31, 81, 171, 393, 799, 1753, 3523}.

LINKS

Table of n, a(n) for n=1..66.

FORMULA

t(n,m)=If[m*(n - m) == 0, 1, (1 + Abs[(1 + n - m) - (1 + m)])*Binomial[n, m]].

EXAMPLE

{1},

{1, 1},

{1, 2, 1},

{1, 6, 6, 1},

{1, 12, 6, 12, 1},

{1, 20, 20, 20, 20, 1},

{1, 30, 45, 20, 45, 30, 1},

{1, 42, 84, 70, 70, 84, 42, 1},

{1, 56, 140, 168, 70, 168, 140, 56, 1},

{1, 72, 216, 336, 252, 252, 336, 216, 72, 1},

{1, 90, 315, 600, 630, 252, 630, 600, 315, 90, 1}

MATHEMATICA

Clear[t, n, m]; t[n_, m_] = If[m*(n - m) == 0, 1, (1 + Abs[(1 + n - m) - (1 + m)])*Binomial[n, m]]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

CROSSREFS

Sequence in context: A283795 A168641 A255914 * A157635 A075798 A155864

Adjacent sequences:  A143182 A143183 A143184 * A143186 A143187 A143188

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 17 2008

STATUS

approved

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Last modified September 24 07:28 EDT 2020. Contains 337317 sequences. (Running on oeis4.)