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Search: id:A118791
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| A118791 |
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Triangle where T(n,k) = -n!*[x^k] ( x/log(1-x-x^2) )^(n+1), for n>=k>=0, read by rows. |
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+0
3
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| 1, -1, 3, 2, -9, 19, -6, 36, -103, 207, 24, -180, 650, -1605, 3211, -120, 1080, -4710, 13860, -32191, 64383, 720, -7560, 38640, -132300, 351722, -790629, 1581259, -5040, 60480, -354480, 1386000, -4163166, 10433556, -22974463, 45948927, 40320, -544320, 3598560, -15830640, 53117064
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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[0, diagonal] = A052886 with e.g.f.: (1-sqrt(5-4*exp(x)))/2. [0, row sums] = A117271 with e.g.f.: log((3-sqrt(5-4*exp(x)))/2). [0, unsigned row sums] = A118792 with e.g.f.: -log((1+sqrt(5-4*exp(x)))/2). Here [0, sequence] indicates that the the sequence is offset with a leading zero.
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EXAMPLE
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Triangle begins:
1;
-1, 3;
2,-9, 19;
-6, 36,-103, 207;
24,-180, 650,-1605, 3211;
-120, 1080,-4710, 13860,-32191, 64383;
720,-7560, 38640,-132300, 351722,-790629, 1581259;
-5040, 60480,-354480, 1386000,-4163166, 10433556,-22974463, 45948927;
which is formed from the powers of F(x) = x/log(1-x-x^2):
F(x)^1 = (-1) + 3/2*x - 11/12*x^2 + 9/8*x^3 - 641/720*x^4 +...
F(x)^2 = ( 1 - 3*x)/1! + 49/12*x^2 - 5*x^3 + 1439/240*x^4 +...
F(x)^3 = (-2 + 9*x - 19*x^2)/2! + 15*x^3 - 5161/240*x^4 +...
F(x)^4 = ( 6 - 36*x + 103*x^2 - 207*x^3)/3! + 42239/720*x^4 +...
F(x)^5 = (-24 + 180*x - 650*x^2 + 1605*x^3 - 3211*x^4)/4! +...
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PROGRAM
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(PARI) {T(n, k)=local(x=X+X^2*O(X^(k+2))); -n!*polcoeff(((x/log(1-x-x^2)))^(n+1), k, X)}
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CROSSREFS
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Cf. A052886 (diagonal), A117271 (row sums), A118792 (unsigned row sums); A118793 (variant).
Sequence in context: A076584 A049969 A088634 this_sequence A049971 A092502 A135515
Adjacent sequences: A118788 A118789 A118790 this_sequence A118792 A118793 A118794
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KEYWORD
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sign,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Apr 30 2006
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