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!)
 A277297 Diagonal of triangle A277295; a(n) = A277295(n+2,n). 5
 2, 14, 76, 378, 1808, 8484, 39446, 182732, 846248, 3926338, 18276832, 85436832, 401313288, 1894847846, 8994916236, 42931067910, 206002472336, 993664391720, 4817140123620, 23464959242520, 114820471485840, 564248307992850, 2783898831160512, 13786409317705920, 68509284536815640, 341538385855855064, 1707729163812908528 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS G.f. G(x,y) of triangle A277295 satisfies: (1) G(x,y) = x + G( y*G(x,y) + (1-y)*x, y)^2. (2) G( x - y*G(x,y)^2, y) = x + (1-y)*G(x,y)^2. LINKS Table of n, a(n) for n=1..27. FORMULA a(n) = 2 * A291822(n) for n >= 1. - Paul D. Hanna, Jul 24 2023 PROG (PARI) {A277295(n, k) = my(A=x); for(i=1, n, A = x + subst(A^2, x, y*A + (1-y)*x +x*O(x^n)) ); polcoeff(polcoeff(A, n, x), k, y)} for(n=1, 30, print1(A277295(n+2, n-1), ", ")) CROSSREFS Cf. A277295, A277296, A277298, A277299, A291822. Sequence in context: A197874 A104871 A172060 * A185055 A034573 A278417 Adjacent sequences: A277294 A277295 A277296 * A277298 A277299 A277300 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 11 2016 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 24 01:38 EDT 2024. Contains 372768 sequences. (Running on oeis4.)