A235391 - OEIS

%I #28 Jul 19 2024 12:02:56

%S 1,1,2,6,21,78,298,1157,4539,17936,71251,284188,1137076,4561093,

%T 18333337,73816489,297635750,1201551286,4855672249,19640147061,

%U 79501958895,322037615290,1305256267511,5293166568270,21475362822956,87166344495561,353933533606927

%N Duplicate of A129775.

%H G. C. Greubel, <a href="/A235391/b235391.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: 1 / (1 - x / (1 - x / (1 - 2*x / (1 - x / (2 - 3*x / (1 - 2*x / (3 - 4*x / ... ))))))).

%F D-finite with recurrence: 0 = (4*n + 6) * a(n) - (17*n + 27) * a(n+1) + (24*n + 42) * a(n+2) - (9*n + 21) * a(n+3) + (n + 3) * a(n+4). - Sign flipped by _R. J. Mathar_, Feb 16 2020

%F 0 = a(n) * (16*a(n+1) - 74*a(n+2) + 120*a(n+3) - 66*a(n+4) + 10*a(n+5))+ a(n+1) * (-62*a(n+1) + 361*a(n+2) - 480*a(n+3) + 265*a(n+4) - 41*a(n+5)) + a(n+2) * (-342*a(n+2) + 615*a(n+3) - 335*a(n+4) + 54*a(n+5)) + a(n+3) * (-90*a(n+3) + 75*a(n+4) - 15*a(n+5)) + a(n+4) * (-3*a(n+4) + a(n+5)).

%F a(n) = A129775(n) if n>0.

%F HANKEL transform is A000012.

%F INVERT transform is A073525.

%e G.f. = 1 + x + 2*x^2 + 6*x^3 + 21*x^4 + 78*x^5 + 298*x^6 + 1157*x^7 + ...

%t a[ n_] := SeriesCoefficient[ 2 / (2 - x - x / Sqrt[1 - 4 x]), {x, 0, n}]

%o (PARI) {a(n) = if( n<0, 0, polcoeff( 2 / (2 - x - x / sqrt(1 - 4*x + x * O(x^n))), n))}

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!(2/( 2-x - x/Sqrt(1-4*x)))); // _G. C. Greubel_, Aug 07 2018

%Y Cf. A000012, A073525, A129775.

%K dead

%O 0,3

%A _Michael Somos_, Jan 09 2014