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Search: id:A117270
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| A117270 |
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Matrix log of triangle M = A117269, which satisfies: M - (M-I)^2 = C where C is Pascal's triangle. |
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+0
3
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| 0, 1, 0, 2, 2, 0, 12, 6, 3, 0, 134, 48, 12, 4, 0, 2100, 670, 120, 20, 5, 0, 42302, 12600, 2010, 240, 30, 6, 0, 1041852, 296114, 44100, 4690, 420, 42, 7, 0, 30331814, 8334816, 1184456, 117600, 9380, 672, 56, 8, 0, 1019056260, 272986326, 37506672, 3553368
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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E.g.f. of column 0 (A117271) is log( (3-sqrt(5-4*exp(x)))/2 ) and equals the log of the g.f. of column 0 of A117269.
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FORMULA
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T(n,k) = A117271(n-k)*C(n,k).
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EXAMPLE
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Triangle begins:
0;
1,0;
2,2,0;
12,6,3,0;
134,48,12,4,0;
2100,670,120,20,5,0;
42302,12600,2010,240,30,6,0;
1041852,296114,44100,4690,420,42,7,0; ...
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PROGRAM
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(PARI) {a(n)=local(C=matrix(n+1, n+1, r, c, if(r>=c, binomial(r-1, c-1))), M=C, L); for(i=1, n+1, M=(M-M^0)^2+C); L=sum(r=1, #M, -(M^0-M)^r/r); return(L[n+1, 1])}
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CROSSREFS
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Cf. A117269, A117271 (column 0).
Sequence in context: A117739 A111810 A019265 this_sequence A091466 A134085 A151339
Adjacent sequences: A117267 A117268 A117269 this_sequence A117271 A117272 A117273
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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), Mar 05 2006
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