The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A137277 Triangle of the coefficients [x^k] P_n(x) of the polynomials P_n(x) = 1/n * sum(j=0..floor(n/2), (-1)^j * binomial(n,j) * (n-4*j) * x^(n-2*j) ). 2
 1, 0, 1, 2, 0, 1, 0, 1, 0, 1, -6, 0, 0, 0, 1, 0, -6, 0, -1, 0, 1, 20, 0, -5, 0, -2, 0, 1, 0, 25, 0, -3, 0, -3, 0, 1, -70, 0, 28, 0, 0, 0, -4, 0, 1, 0, -98, 0, 28, 0, 4, 0, -5, 0, 1, 252, 0, -126, 0, 24, 0, 9, 0, -6, 0, 1, 0, 378, 0, -150, 0, 15, 0, 15, 0, -7, 0, 1, -924, 0, 528, 0, -165, 0, 0, 0, 22, 0, -8, 0, 1, 0, -1452 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The first four P_n(x) are the same as in A137276. Row sums are 1, 1, 3, 2, -5, -6, 14, 20, -45, -70, 154, a signed variant of A047074. LINKS Table of n, a(n) for n=0..92. FORMULA P(0,n)=1. P_n(x) = 1/n*sum(j=0..floor(n/2), (-1)^j*binomial(n,j)*(n-4*j)*x^(n-2*j)). EXAMPLE {1}, = 1 {0, 1}, = x {2, 0, 1}, = 2+x^2 {0, 1, 0, 1}, = x+x^3 {-6, 0, 0, 0, 1}, = -6+x^4 {0, -6, 0, -1, 0, 1}, {20, 0, -5, 0, -2, 0, 1}, {0, 25, 0, -3,0, -3, 0, 1}, {-70, 0, 28, 0, 0, 0, -4, 0, 1}, {0, -98, 0, 28, 0,4, 0, -5, 0, 1}, {252, 0, -126, 0, 24, 0, 9, 0, -6, 0, 1} MAPLE A137277 := proc(n, k) if n = 0 then 1; else add( (-1)^j*binomial(n, j)*(n-4*j)*x^(n-2*j), j=0..n/2)/n ; coeftayl(%, x=0, k) ; fi; end: seq( seq(A137277(n, k), k=0..n), n=0..15) ; MATHEMATICA B[x_, n_] = If[n > 0, Sum[(-1)^p*Binomial[n, p]*(n - 4*p)*x^(n - 2*p)/ n, {p, 0, Floor[n/2]}], 1]; a = Table[CoefficientList[B[x, n], x], {n, 0, 10}]; Flatten[a] CROSSREFS Cf. A138034. Sequence in context: A287234 A309938 A140581 * A039975 A358679 A016253 Adjacent sequences: A137274 A137275 A137276 * A137278 A137279 A137280 KEYWORD sign,easy,tabl AUTHOR Roger L. Bagula, Mar 13 2008 EXTENSIONS Edited by the Associate Editors of the OEIS, Aug 27 2009 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 May 19 06:35 EDT 2024. Contains 372666 sequences. (Running on oeis4.)