A382647 Expansion of 1/(1 - x*(1 + 4*x)^(1/2))^2.

1, 2, 7, 12, 37, 50, 187, 128, 1057, -502, 7679, -14420, 73453, -212554, 843019, -2848064, 10602409, -37875706, 139533151, -510006524, 1885309253, -6974175142, 25940881947, -96731191728, 361980829841, -1358121976978, 5109416286295, -19267391982612

Offset: 0

Author

Seiichi Manyama, Apr 02 2025

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..600

Crossrefs

Cf. A382539, A382649.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 28); Coefficients(R!( 1/(1 - x*(1 + 4*x)^(1/2))^2)); // Vincenzo Librandi, May 13 2025

Mathematica

Table[Sum[4^(n-k)* (k+1)* Binomial[k/2, n-k],{k,0,n}],{n,0,28}] (* Vincenzo Librandi, May 13 2025 *)

PARI

a(n) = sum(k=0, n, 4^(n-k)*(k+1)*binomial(k/2, n-k));

Formula

a(n) = Sum_{k=0..n} 4^(n-k) * (k+1) * binomial(k/2,n-k).