A382514 Expansion of 1/(1 - x/(1 - 4*x)^(3/2)).
1, 1, 7, 43, 255, 1493, 8695, 50517, 293163, 1700335, 9859019, 57156631, 331332423, 1920621431, 11132911939, 64531189379, 374047777319, 2168115796941, 12567146992975, 72843402779669, 422224417571347, 2447350774345341, 14185640454054279, 82224565359415849
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
Programs
-
Magma
R
:= PowerSeriesRing(Rationals(), 40); f := 1/(1 - x/(1 - 4*x)^(3/2)); seq := [ Coefficient(f, n) : n in [0..30] ]; seq; // Vincenzo Librandi, Apr 09 2025 -
Mathematica
Table[Sum[4^(n-k)*Binomial[n+k/2-1,n-k],{k,0,n}],{n,0,35}] (* Vincenzo Librandi, Apr 09 2025 *) -
PARI
a(n) = sum(k=0, n, 4^(n-k)*binomial(n+k/2-1, n-k));
Formula
a(n) = Sum_{k=0..n} 4^(n-k) * binomial(n+k/2-1,n-k).
D-finite with recurrence (-n+1)*a(n) +2*(8*n-13)*a(n-1) +5*(-19*n+43)*a(n-2) +2*(126*n-361)*a(n-3) +128*(-2*n+7)*a(n-4)=0. - R. J. Mathar, Mar 31 2025