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).

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

Links

Table of n, a(n) for n=1..78.

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

Adjacent sequences: A183188 A183189 A183190 * A183192 A183193 A183194

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Dec 15 2011

Status

approved