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 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}. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS 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

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Last modified March 21 07:23 EDT 2019. Contains 321367 sequences. (Running on oeis4.)