A129855 A symmetrical triangle of coefficients based on A000217: a(n) = Binomial[n + 2, 2]; t(n,m)=a(n - m + 1)*a(m + 1).

9, 18, 18, 30, 36, 30, 45, 60, 60, 45, 63, 90, 100, 90, 63, 84, 126, 150, 150, 126, 84, 108, 168, 210, 225, 210, 168, 108, 135, 216, 280, 315, 315, 280, 216, 135, 165, 270, 360, 420, 441, 420, 360, 270, 165, 198, 330, 450, 540, 588, 588, 540, 450, 330, 198, 234

Offset

1,1

Comments

Row sums are:

{9, 36, 96, 210, 406, 720, 1197, 1892, 2871, 4212, 6006}.

References

G. E. Andrews, Number Theory, 1971, Dover Publications New York, p 44.

Links

Table of n, a(n) for n=1..56.

Formula

a(n) = Binomial[n + 2, 2]; t(n,m)=a(n - m + 1)*a(m + 1).

Example

{9},
{18, 18},
{30, 36, 30},
{45, 60, 60, 45},
{63, 90, 100, 90, 63},
{84, 126, 150, 150, 126, 84},
{108, 168, 210, 225, 210, 168, 108},
{135, 216, 280, 315, 315, 280, 216, 135},
{165, 270, 360, 420, 441, 420, 360, 270, 165},
{198, 330, 450, 540, 588, 588, 540, 450, 330, 198},
{234, 396, 550, 675, 756, 784, 756, 675, 550, 396, 234}

Mathematica

Clear[a, n, m, t] (*A000217*) a[0] = 1; a[1] = 3; a[n_] := a[n] = Binomial[n + 2, 2]; Table[a[n], {n, 0, 30}]; t[n_, m_] = a[n - m + 1]*a[m + 1]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Crossrefs

Cf. A000217.

Sequence in context: A046125 A040072 A034728 * A250769 A158908 A202188

Adjacent sequences: A129852 A129853 A129854 * A129856 A129857 A129858

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Aug 25 2008

Status

approved