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A183191
Triangle T(n,m) = coefficient of x^n in expansion of [x/(1-x-x^2-x^3-x^4-2*x^5)]^m = sum(n>=m, T(n,m) x^n).
0
1, 1, 1, 2, 2, 1, 4, 5, 3, 1, 8, 12, 9, 4, 1, 17, 28, 25, 14, 5, 1, 33, 66, 66, 44, 20, 6, 1, 66, 148, 171, 129, 70, 27, 7, 1, 132, 330, 425, 364, 225, 104, 35, 8, 1, 264, 728, 1035, 984, 686, 363, 147, 44, 9, 1, 529, 1592, 2475, 2584, 1995, 1188, 553, 200, 54, 10, 1, 1057, 3459, 5830, 6624, 5600, 3689, 1932, 806, 264, 65, 11, 1
OFFSET
1,4
FORMULA
T(n,i):=sum(k=0..n-i, binomial(k+i-1,i-1)*sum(r=0..k, binomial(k,r)*sum(m=0..r, binomial(r,m)*sum(j=0..m, binomial(j,-r+n-m-k-j-i)*binomial(m,j)*2^(-r+n-m-k-j-i))))).
EXAMPLE
1,
1, 1,
2, 2, 1,
4, 5, 3, 1,
8, 12, 9, 4, 1,
17, 28, 25, 14, 5, 1,
33, 66, 66, 44, 20, 6, 1,
PROG
(Maxima)
T(n, i):=sum(binomial(k+i-1, i-1)*sum(binomial(k, r)*sum(binomial(r, m)*sum(binomial(j, -r+n-m-k-j-i)*binomial(m, j)*2^(-r+n-m-k-j-i), j, 0, m), m, 0, r), r, 0, k), k, 0, n-i);
CROSSREFS
Sequence in context: A104580 A202193 A105306 * A273713 A339067 A322329
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Dec 15 2011
STATUS
approved