A118791 Triangle where T(n,k) = -n!*[x^k] ( x/log(1-x-x^2) )^(n+1), for n>=k>=0, read by rows.
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
Offset: 0
Examples
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! +...
Crossrefs
Programs
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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)}
Comments