A089722 Triangle T(n,k), 0<=k<=n, read by rows, defined by: Product{k=1..n, (1+x^k)^(n+1-k)} = Sum{k>=0, T(n,k)*x^k}.

1, 1, 1, 1, 2, 2, 2, 1, 1, 3, 5, 8, 10, 10, 10, 8, 5, 3, 1, 1, 4, 9, 18, 31, 46, 64, 82, 96, 106, 110, 106, 96, 82, 64, 46, 31, 18, 9, 4, 1, 1, 5, 14, 33, 68, 124, 210, 332, 492, 693, 931, 1196, 1476, 1754, 2008, 2220, 2374, 2453, 2453, 2374, 2220, 2008, 1754, 1476, 1196

Offset

0,5

Links

Table of n, a(n) for n=0..64.

Formula

T(n, k) = Sum {a_1, a_2, ...a_n with a_1+2*a_2+...+n*a_n=k, C(n, a_1)*C(n-1, a_2)*...*C(1, a_n)} .

Sum_{k, k>=0} T(n, k) = 2^(n*(n+1)/2), see A006125.

Example

Row n=0 : 1
Row n=1 : 1, 1
Row n=2 : 1, 2, 2, 2, 1
Row n=3 : 1, 3, 5, 8, 10, 10, 10, 8, 5, 3, 1
Row n=4 : 1, 4, 9, 18, 31, 46, 64, 82, 96, 106, 110, 106, 96, 82, 64, 46, 31, 18, 9, 4, 1

Crossrefs

Cf. A006125.

Sequence in context: A193884 A128084 A131823 * A172356 A184948 A242775

Adjacent sequences: A089719 A089720 A089721 * A089723 A089724 A089725

Keyword

easy,nonn,tabf

Author

Philippe Deléham, Jan 06 2004, Oct 16 2008

Status

approved