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

0,2

Links

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

Formula

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

Mathematica

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

Prog

(PARI) a(n) = sum(k=0, n, 4^(n-k)*(k+1)*binomial(k/2, n-k));
(Magma) R<x>:=PowerSeriesRing(Rationals(), 28); Coefficients(R!( 1/(1 - x*(1 + 4*x)^(1/2))^2)); // Vincenzo Librandi, May 13 2025

Crossrefs

Cf. A382539, A382649.

Sequence in context: A326026 A092831 A055257 * A238366 A084068 A192772

Adjacent sequences: A382644 A382645 A382646 * A382648 A382649 A382650

Keyword

sign,easy

Author

Seiichi Manyama, Apr 02 2025

Status

approved