A128821 Triangle T(n,k), 1<=k<=n, read by rows defined by :T(n,k)=C(n,k)*C(n-1,k-1)+C(n,k-1)*C(n-1,k)where C(n,k)=A007318(n,k) .

1, 3, 1, 5, 9, 1, 7, 30, 18, 1, 9, 70, 100, 30, 1, 11, 135, 350, 250, 45, 1, 13, 231, 945, 1225, 525, 63, 1, 15, 364, 2156, 4410, 3430, 980, 84, 1, 17, 540, 4368, 12936, 15876, 8232, 1680, 108, 1, 19, 765, 8100, 32760, 58212, 47628, 17640, 2700, 135, 1

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Formula

T(n,k)=A001263(n,k)*(2n-2k+1). Sum_{k, 1<=k<=n}T(n,k)=binomial(2n,n-1)=A001791(n). T(2n-1,n)=A060150(n), n>=1 .

Example

Triangle begins:
1;
3, 1;
5, 9, 1;
7, 30, 18, 1;
9, 70, 100, 30, 1;
11, 135, 350, 250, 45, 1;
13, 231, 945, 1225, 525, 63, 1;
15, 364, 2156, 4410, 3430, 980, 84, 1 ;...

Crossrefs

Cf. A005408, A002414.

Sequence in context: A240222 A193702 A193710 * A221446 A029723 A187370

Adjacent sequences: A128818 A128819 A128820 * A128822 A128823 A128824

Keyword

nonn,tabl

Author

Philippe Deléham, Apr 11 2007

Status

approved