A271460 Triangle read by rows: T(n,m) = (m/(n-m))*Sum_{k=1..n-m}((-1)^k*binomial(m-1,k-1)*binomial(3*(n-m)-k-1,n-m-k)), T(n,n)=1.

1, -1, 1, -2, -2, 1, -7, -3, -3, 1, -30, -10, -3, -4, 1, -143, -42, -10, -2, -5, 1, -728, -198, -42, -8, 0, -6, 1, -3876, -1001, -198, -35, -5, 3, -7, 1, -21318, -5304, -1001, -168, -25, -2, 7, -8, 1, -120175, -29070, -5304, -858, -126, -15, 0, 12, -9, 1

Offset

1,4

Links

Table of n, a(n) for n=1..55.

Formula

G.f.: -1+1/(1-x*y+x*y*(4*sin(asin((3^(3/2)*sqrt(x))/2)/3)^2)/3)

T(n,m) = (1/(n-m))*(m*(-1)^(n-m)*Sum_{k=1..n-m} binomial(k-1,n-m-1)*binomial(-2*n+3*m-1,k-1)*binomial(3*n-4*m,n-m-k)), n>m, T(n,n)=1

Example

1;
-1,1;
-2,-2,1;
-7,-3,-3,1;
-30,-10,-3,-4,1;
-143,-42,-10,-2,-5,1;
-728,-198,-42,-8,0,-6,1;

Prog

(Maxima)
T(n, m):=if n=m then 1 else m*(-1)^(n-m)/(n-m)*sum((binomial(k-1, n-m-1)*binomial(-2*n+3*m-1, k-1)*binomial(3*n-4*m, n-m-k)), k, 1, n-m);

Crossrefs

Cf. A006013.

Sequence in context: A340734 A108338 A021455 * A248924 A307455 A136502

Adjacent sequences: A271457 A271458 A271459 * A271461 A271462 A271463

Keyword

sign,tabl

Author

Vladimir Kruchinin, Apr 13 2016

Status

approved