A202483 Triangle T(n,m) = coefficient of x^n in expansion of [(1-(1-9*x)^(1/3))/(4-(1-9*x)^(1/3))]^m = sum(n>=m, T(n,m) x^n).

1, 2, 1, 10, 4, 1, 59, 24, 6, 1, 385, 158, 42, 8, 1, 2672, 1106, 305, 64, 10, 1, 19336, 8064, 2283, 508, 90, 12, 1, 144218, 60541, 17484, 4052, 775, 120, 14, 1, 1100530, 464650, 136315, 32560, 6565, 1114, 154, 16, 1

Offset

1,2

Comments

The matrix inverse starts

1;

-2,1;

-2,-4,1;

1,0,-6,1;

7,10,6,-8,1;

16,14,19,16,-10,1;

28,0,-3,20,30,-12,1;

43,-35,-60,-52,5,48,-14,1;

61,-76,-89,-112,-125,-34,70,-16,1; - R. J. Mathar, Mar 22 2013

Links

Table of n, a(n) for n=1..45.

Formula

T(n,m)=sum(i=m..n, i*(-1)^(i-m) *binomial(i-1,m-1) *sum(k=0..n-i, binomial(k,n-k-i) *3^k *(-1)^(n-k-i) *binomial(n+k-1,n-1)))/n.

Example

1
2, 1,
10, 4, 1,
59, 24, 6, 1,
385, 158, 42, 8, 1,
2672, 1106, 305, 64, 10, 1,
19336, 8064, 2283, 508, 90, 12, 1

Maple

A202483 := proc(n, m)
    if m < 1 or m > n then
        0;
    else
        a := 0 ;
        for i from m to n do
         a := a+ i*(-1)^(i-m)*binomial(i-1, m-1) *add( binomial(k, n-k-i) *3^k *(-1)^(n-k-i) *binomial(n+k-1, n-1), k=0..n-i) ;
        end do:
        return a/n ;
    end if;
end proc: # R. J. Mathar, Mar 22 2013

Prog

(Maxima)
T(n, m):=sum(i*(-1)^(i-m)*binomial(i-1, m-1)*sum(binomial(k, n-k-i)*3^(k)*(-1)^(n-k-i)*binomial(n+k-1, n-1), k, 0, n-i), i, m, n)/n;

Crossrefs

Sequence in context: A163235 A142963 A099755 * A110682 A110327 A105615

Adjacent sequences: A202480 A202481 A202482 * A202484 A202485 A202486

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Dec 20 2011

Status

approved