The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A112466 Riordan array ((1+2x)/(1+x), x/(1+x)). 4
 1, 1, 1, -1, 0, 1, 1, -1, -1, 1, -1, 2, 0, -2, 1, 1, -3, 2, 2, -3, 1, -1, 4, -5, 0, 5, -4, 1, 1, -5, 9, -5, -5, 9, -5, 1, -1, 6, -14, 14, 0, -14, 14, -6, 1, 1, -7, 20, -28, 14, 14, -28, 20, -7, 1, -1, 8, -27, 48, -42, 0, 42, -48, 27, -8, 1, 1, -9, 35, -75, 90, -42, -42, 90, -75, 35, -9, 1, -1, 10, -44, 110, -165, 132, 0, -132, 165, -110, 44 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 COMMENTS Row sums are (1,2,0,0,0,...). Inverse is A112465. Triangle T(n,k), 0 <= k <= n, read by rows, given by [1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, Aug 07 2006; corrected by Philippe Deléham, Dec 11 2008 LINKS Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows 0 <= n <= 150, flattened) Paul Barry, A Note on Riordan Arrays with Catalan Halves, arXiv:1912.01124 [math.CO], 2019. E. Deutsch, L. Ferrari and S. Rinaldi, Production Matrices, Advances in Mathematics, 34 (2005) pp. 101-122. FORMULA Number triangle T(n,k) = (-1)^(n-k)*(C(n, n-k) - 2*C(n-1, n-k-1)). Sum_{k=0..floor(n/2)} T(n-k,k) = (-1)^(n+1)*Fibonacci(n-2). T(2n,n) = 0. Sum_{k=0..n} T(n,k)*x^k = (x+1)*(x-1)^(n-1), for n >= 1. - Philippe Deléham, Oct 03 2005 T(0,0)=T(1,0)=T(1,1)=1, T(n,k)=0 if n < 0 or if n < k, T(n,k) = T(n-1,k-1) - T(n-1,k) for n > 1. - Philippe Deléham, Nov 26 2006 G.f.: (1+2*x)/(1+x-x*y). - R. J. Mathar, Aug 11 2015 EXAMPLE Triangle starts 1; 1, 1; -1, 0, 1; 1, -1, -1, 1; -1, 2, 0, -2, 1; 1, -3, 2, 2, -3, 1; -1, 4, -5, 0, 5, -4, 1; From Paul Barry, Apr 08 2011: (Start) Production matrix begins 1, 1; -2, -1, 1; 2, 0, -1, 1; -2, 0, 0, -1, 1; 2, 0, 0, 0, -1, 1; -2, 0, 0, 0, 0, -1, 1; 2, 0, 0, 0, 0, 0, -1, 1; (End) MAPLE seq(seq( (-1)^(n-k)*(2*binomial(n-1, k-1)-binomial(n, k)), k=0..n), n=0..10); # G. C. Greubel, Feb 19 2020 MATHEMATICA {1}~Join~Table[(Binomial[n, n - k] - 2 Binomial[n - 1, n - k - 1])*(-1)^(n - k), {n, 12}, {k, 0, n}] // Flatten (* Michael De Vlieger, Feb 18 2020 *) PROG (PARI) T(n, k) = (-1)^(n-k)*(binomial(n, n-k) - 2*binomial(n-1, n-k-1)); \\ Michel Marcus, Feb 19 2020 CROSSREFS Cf. A008482, A037012, A097808, A112467. Sequence in context: A008482 A037012 A112467 * A166348 A294658 A127543 Adjacent sequences: A112463 A112464 A112465 * A112467 A112468 A112469 KEYWORD easy,sign,tabl AUTHOR Paul Barry, Sep 06 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 06:48 EST 2022. Contains 358595 sequences. (Running on oeis4.)