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Search: id:A105626
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| A105626 |
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Triangular matrix T, read by rows, that satisfies T^2 = A105615^3; also equals the matrix cube of triangle A105623. |
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+0
3
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| 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
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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SHIFT_LEFT(column 0 of T) = 3*(column 2 of A105615). A105623 equals the matrix square-root of triangle A105615.
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FORMULA
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T(n+1, 0) = 3*A105615(n+2, 2) = 3*A105617(n) for n>=0.
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EXAMPLE
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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; ...
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PROGRAM
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(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]))}
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CROSSREFS
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Cf. A105615, A105617, A105623, A105627 (column 1), A105628 (row sums).
Sequence in context: A096611 A060281 A089974 this_sequence A071210 A051141 A068141
Adjacent sequences: A105623 A105624 A105625 this_sequence A105627 A105628 A105629
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 2005
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