A105626 Triangular matrix T, read by rows, that satisfies T^2 = A105615^3; also equals the matrix cube of triangle A105623.

1, 3, 1, 18, 6, 1, 150, 48, 9, 1, 1566, 480, 93, 12, 1, 19494, 5736, 1125, 153, 15, 1, 280998, 79584, 15681, 2190, 228, 18, 1, 4598910, 1256808, 247929, 35181, 3780, 318, 21, 1, 84237246, 22262640, 4389213, 629424, 68961, 6000, 423, 24, 1, 1707637734

Offset

0,2

Comments

SHIFT_LEFT(column 0 of T) = 3*(column 2 of A105615). A105623 equals the matrix square-root of triangle A105615.

Links

Table of n, a(n) for n=0..45.

Formula

T(n+1, 0) = 3*A105615(n+2, 2) = 3*A105617(n) for n>=0.

Example

Triangle begins:
1;
3,1;
18,6,1;
150,48,9,1;
1566,480,93,12,1;
19494,5736,1125,153,15,1;
280998,79584,15681,2190,228,18,1;
4598910,1256808,247929,35181,3780,318,21,1;
84237246,22262640,4389213,629424,68961,6000,423,24,1; ...

Prog

(PARI) T(n, k)=local(R, M=matrix(n+1, n+1, m, j, if(m>=j, if(m==j, 1, if(m==j+1, -2*j, polcoeff(1/sum(i=0, m-j, (2*i)!/i!/2^i*x^i)+O(x^m), m-j)))))^-3); R=(M+M^0)/2; for(i=1, floor(2*log(n+2)), R=(R+M*R^(-1))/2); return(if(n<k || k<0, 0, R[n+1, k+1]))

Crossrefs

Cf. A105615, A105617, A105623, A105627 (column 1), A105628 (row sums).

Sequence in context: A143849 A370233 A335689 * A071210 A051141 A068141

Adjacent sequences: A105623 A105624 A105625 * A105627 A105628 A105629

Keyword

nonn,tabl

Author

Paul D. Hanna, Apr 16 2005

Status

approved