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Search: id:A107719
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| 1, 1, 1, 5, 2, 1, 43, 13, 3, 1, 509, 131, 25, 4, 1, 7579, 1741, 303, 41, 5, 1, 135341, 28451, 4681, 587, 61, 6, 1, 2813851, 549757, 87039, 10449, 1011, 85, 7, 1, 66733853, 12247211, 1885177, 220023, 20445, 1603, 113, 8, 1, 1778159275, 308953453
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Column 0 is A107720. Column 1 is A107721. Matrix inverse is A107727.
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EXAMPLE
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Triangle begins:
1;
1,1;
5,2,1;
43,13,3,1;
509,131,25,4,1;
7579,1741,303,41,5,1;
135341,28451,4681,587,61,6,1;
2813851,549757,87039,10449,1011,85,7,1; ...
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PROGRAM
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(PARI)
(PARI) {T(n, k)=local(E, L, M=matrix(n+1, n+1, m, j, if(m>=j, if(m==j, 1, if(m==j+1, -3*j, -polcoeff(1-(1+sum(c=1, m-j, prod(i=0, c-1, 3*i+1)*x^c)+x*O(x^(m-j)))^-1, m-j); ))))^-1); L=matrix(#M, #M, r, c, if(r>=c, sum(i=1, #M, (-1)^(i-1)*(M-M^0)^i/i)[r, c])); E=matrix(#L, #L, r, c, if(r>=c, sum(i=0, #L, L^i/3^i/i!)[r, c])); if(n<k|k<0, 0, E[n+1, k+1])}
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CROSSREFS
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Cf. A107717, A107720, A107721, A107727.
Sequence in context: A111544 A109281 A133289 this_sequence A021661 A058841 A129165
Adjacent sequences: A107716 A107717 A107718 this_sequence A107720 A107721 A107722
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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), May 30 2005
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