A143081 A symmetrical triangle of coefficients based on A001147: a(n)=(2*n-1)*a(n-1); t(n,m)=a(n)^2/((2*n - 1)*a(m)*a(n - m)).

-1, 1, 1, 1, 3, 1, 3, 15, 15, 3, 15, 105, 175, 105, 15, 105, 945, 2205, 2205, 945, 105, 945, 10395, 31185, 43659, 31185, 10395, 945, 10395, 135135, 495495, 891891, 891891, 495495, 135135, 10395, 135135, 2027025, 8783775, 19324305, 24845535, 19324305, 8783775, 2027025, 135135, 2027025, 34459425

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Oct 15 2008

Keywords

• uned
• sign

Comments

Row sums are:{-1, 2, 5, 36, 415, 6510, 128709, 3065832, 85386015, 2721425850, 97665121125}.

Examples

			{-1},
{1, 1},
{1, 3, 1},
{3, 15, 15, 3},
{15, 105, 175, 105, 15},
{105, 945, 2205, 2205, 945, 105},
{945, 10395, 31185, 43659, 31185, 10395, 945},
{10395, 135135, 495495, 891891, 891891, 495495, 135135, 10395},
{135135, 2027025, 8783775, 19324305, 24845535, 19324305, 8783775, 2027025, 135135},
{2027025, 34459425, 172297125, 447972525, 703956825, 703956825, 447972525, 172297125, 34459425, 2027025}, {34459425, 654729075, 3710131425, 11130394275,
20670732225, 25264228275, 20670732225, 11130394275, 3710131425, 654729075,
34459425}
		

Crossrefs

Cf. A001147.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = (2*n - 1)*a[n - 1]; Table[Table[a[n]^2/((2*n - 1)*a[m]*a[n - m]), {m, 0, n}], {n, 0, 10}]; Flatten[%]

Formula

a(n)=(2*n-1)*a(n-1); t(n,m)=a(n)^2/((2*n - 1)*a(m)*a(n - m)).