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!)
 A370051 Expansion of (1-5*x+6*x^2-x^3)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5). 2
 1, 4, 14, 48, 165, 572, 2002, 7071, 25176, 90251, 325358, 1178291, 4282811, 15612092, 57040186, 208772476, 765186422, 2807556411, 10309833845, 37883902913, 139275229088, 512223805060, 1884404481767, 6934058102453, 25519786076294 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In Pascal's triangle, subtract the 6th column to the left of the central column from the 2nd column. LINKS Table of n, a(n) for n=0..24. Index entries for linear recurrences with constant coefficients, signature (9,-28,35,-15,1). FORMULA a(n) = 9*a(n-1) - 28*a(n-2) + 35*a(n-3) - 15*a(n-4) + a(n-5); a(0) = 1, a(1) = 4, a(2) = 14, a(3) = 48, a(4) = 165. EXAMPLE a(0) = binomial(2,0); a(1) = binomial(4,1); a(2) = binomial(6,2) - binomial(6,0); a(3) = binomial(8,3) - binomial(8,1); a(4) = binomial(10,4) - binomial(10,2). MATHEMATICA LinearRecurrence[{9, -28, 35, -15, 1}, {1, 4, 14, 48, 165}, 30] (* Paolo Xausa, Feb 20 2024 *) CROSSREFS Cf. A007318, A211216, A224422, A221863, A122588. Sequence in context: A092489 A094827 A094667 * A099376 A002057 A047048 Adjacent sequences: A370048 A370049 A370050 * A370052 A370053 A370054 KEYWORD nonn,easy AUTHOR Peter Morris, Feb 08 2024 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 20 14:08 EDT 2024. Contains 372717 sequences. (Running on oeis4.)