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A105623
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Matrix square-root of triangle A105615.
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9
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Column 0 equals A105616 (=column 1 of A105615) shift 1 place right. Column 1 is A000698 (related to double factorials) offset 1.
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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; ...
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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]))}
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CROSSREFS
| Cf. A105615, A105616 (column 0), A000698 (column 1), A105620 (matrix inverse).
Sequence in context: A111536 A111559 A152406 * A158835 A138271 A136212
Adjacent sequences: A105620 A105621 A105622 * A105624 A105625 A105626
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 2005
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