A107727 Matrix inverse of A107719.

1, -1, 1, -3, -2, 1, -21, -7, -3, 1, -219, -53, -13, -4, 1, -2973, -583, -115, -21, -5, 1, -49323, -8249, -1437, -217, -31, -6, 1, -964173, -141655, -22715, -3101, -369, -43, -7, 1, -21680571, -2853185, -430877, -55251, -5975, -581, -57, -8, 1, -551173053, -65887783, -9505707, -1168349, -119137

Offset

0,4

Comments

Matrix square is A107728. Matrix cube is A107726. Column 0 is negative A107716 shift right.

Links

Table of n, a(n) for n=0..49.

Example

Triangle begins:
1;
-1,1;
-3,-2,1;
-21,-7,-3,1;
-219,-53,-13,-4,1;
-2973,-583,-115,-21,-5,1;
-49323,-8249,-1437,-217,-31,-6,1;
-964173,-141655,-22715,-3101,-369,-43,-7,1; ...

Prog

(PARI) {T(n, k)=local(L, N, M=matrix(n+1, n+1, m, j, if(m>=j, if(m==j, 1, if(m==j+1, -3*j, polcoeff(1/sum(i=0, m-j, prod(r=0, i-1, 3*r+1)*x^i)+O(x^m), m-j)))))^-1); L=sum(i=1, #M, (M^0-M)^i/i)/3; N=sum(i=0, #L, L^i/i!); return(if(n<0, 0, N[n+1, k+1]))}

Crossrefs

Cf. A107716, A107719, A107726, A107728.

Sequence in context: A291080 A107862 A117265 * A346743 A087041 A357675

Adjacent sequences: A107724 A107725 A107726 * A107728 A107729 A107730

Keyword

sign,tabl

Author

Paul D. Hanna, May 30 2005

Status

approved