

A174093


A symmetrical triangle sequence as polynomial coefficients:t(n,k)=If[n == 0  n == 1, 1, Binomial[n  k + 1, k] + Binomial[k + 1, (n  k)]]


0



1, 1, 1, 1, 4, 1, 1, 4, 4, 1, 1, 4, 6, 4, 1, 1, 5, 7, 7, 5, 1, 1, 6, 10, 8, 10, 6, 1, 1, 7, 15, 11, 11, 15, 7, 1, 1, 8, 21, 20, 10, 20, 21, 8, 1, 1, 9, 28, 35, 16, 16, 35, 28, 9, 1, 1, 10, 36, 56, 35, 12, 35, 56, 36, 10, 1
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OFFSET

0,5


COMMENTS

Row sums are:
{1, 2, 6, 10, 16, 26, 42, 68, 110, 178, 288,...}.


LINKS

Table of n, a(n) for n=0..65.


FORMULA

t(n,k)=If[n == 0  n == 1, 1, Binomial[n  k + 1, k] + Binomial[k + 1, (n  k)]]


EXAMPLE

{1},
{1, 1},
{1, 4, 1},
{1, 4, 4, 1},
{1, 4, 6, 4, 1},
{1, 5, 7, 7, 5, 1},
{1, 6, 10, 8, 10, 6, 1},
{1, 7, 15, 11, 11, 15, 7, 1},
{1, 8, 21, 20, 10, 20, 21, 8, 1},
{1, 9, 28, 35, 16, 16, 35, 28, 9, 1},
{1, 10, 36, 56, 35, 12, 35, 56, 36, 10, 1}


MATHEMATICA

f[n_, k_] = If[n == 0  n == 1, 1, Binomial[n  k + 1, k] + Binomial[k + 1, (n  k)]] Table[CoefficientList[Sum[f[n, k]*x^k, {k, 0, n}], x], {n, 0, 10}] Flatten[%]


CROSSREFS

Cf. A011973
Sequence in context: A053239 A046569 A046596 * A204028 A106314 A152716
Adjacent sequences: A174090 A174091 A174092 * A174094 A174095 A174096


KEYWORD

nonn,tabl,uned


AUTHOR

Roger L. Bagula, Mar 07 2010


STATUS

approved



