The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A110330 Inverse of a number triangle related to the Pell numbers. 6
 1, -2, 1, -2, -4, 1, 0, -6, -6, 1, 0, 0, -12, -8, 1, 0, 0, 0, -20, -10, 1, 0, 0, 0, 0, -30, -12, 1, 0, 0, 0, 0, 0, -42, -14, 1, 0, 0, 0, 0, 0, 0, -56, -16, 1, 0, 0, 0, 0, 0, 0, 0, -72, -18, 1, 0, 0, 0, 0, 0, 0, 0, 0, -90, -20, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -110, -22, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -132, -24, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This is the matrix inverse of A110327. Row sums are A110331. Diagonal sums are A110322. Inverse of A110327. The result can be generalized as follows: The triangle whose columns have e.g.f. (x^k/k!)/(1-a*x-b*x^2) has inverse T(n,k)=if(n=k,1,if(n-k=1,-a*binomial(n,1),if(n-k=2,-2*b*binomial(n,2),0))). LINKS FORMULA T(n,k) = if(n=k, 1, if(n-k=1, -2*binomial(n, 1), if(n-k=2, -2*binomial(n, 2), 0))). E.g.f.: exp(x*y)(1-2x-x^2). This implies that the row polynomials form an Appell sequence. - Tom Copeland, Dec 02 2013 EXAMPLE Rows begin 1; -2,1; -2,-4,1; 0,-6,-6,1; 0,0,-12,-8,1; 0,0,0,-20,-10,1; 0,0,0,0,-30,-12,1; MATHEMATICA T[n_, k_] := Which[n == k, 1, n-k == 1, -2*Binomial[n, 1], n-k == 2, -2*Binomial[n, 2], True, 0]; Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 09 2015 *) PROG (PARI) {(T(n, k) = if(n==k, 1, if(n-k==1, -2*binomial(n, 1), if(n-k==2, -2*binomial(n, 2), 0)))); triangle(nMax) = for (n=0, nMax, for (k=0, n, print1(T(n, k), ", ")); print()); } \\ Michel Marcus, Dec 02 2013 (PARI) egfxy(n, k) = {x = xx + xx*O(xx^n); y = yy + yy*O(yy^k); n!*polcoeff(polcoeff(exp(x*y)*(1-2*x-x^2), n, xx), k, yy); } \\ Michel Marcus, Dec 02 2013 CROSSREFS Sequence in context: A181302 A304785 A143446 * A132014 A097864 A097866 Adjacent sequences:  A110327 A110328 A110329 * A110331 A110332 A110333 KEYWORD easy,sign,tabl AUTHOR Paul Barry, Jul 20 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 4 15:50 EDT 2020. Contains 336202 sequences. (Running on oeis4.)