A105623 Matrix square-root of triangle A105615.

1, 1, 1, 4, 2, 1, 26, 10, 3, 1, 226, 74, 19, 4, 1, 2426, 706, 167, 31, 5, 1, 30826, 8162, 1831, 320, 46, 6, 1, 451586, 110410, 23843, 4021, 548, 64, 7, 1, 7489426, 1708394, 358339, 59024, 7801, 866, 85, 8, 1, 138722426, 29752066, 6097607, 987763, 127985

Offset

0,4

Comments

Column 0 equals A105616 (=column 1 of A105615) shift 1 place right. Column 1 is A000698 (related to double factorials) offset 1.

Links

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

Example

Triangle begins:
1;
1,1;
4,2,1;
26,10,3,1;
226,74,19,4,1;
2426,706,167,31,5,1;
30826,8162,1831,320,46,6,1;
451586,110410,23843,4021,548,64,7,1;
7489426,1708394,358339,59024,7801,866,85,8,1;
138722426,29752066,6097607,987763,127985,13801,1289,109,9,1; ...

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)))))^-1); 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, A105616 (column 0), A000698 (column 1), A105620 (matrix inverse).

Sequence in context: A224798 A239894 A152406 * A364870 A158835 A236961

Adjacent sequences: A105620 A105621 A105622 * A105624 A105625 A105626

Keyword

nonn,tabl

Author

Paul D. Hanna, Apr 16 2005

Status

approved