A104531 Expansion of (1+sqrt(1-4*x))/(5*sqrt(1-4*x)-3).

1, 4, 24, 148, 920, 5736, 35808, 223668, 1397496, 8732920, 54575888, 341082504, 2131706864, 13322959888, 83267756400, 520420803060, 3252620324280, 20328841669080, 127055130786960, 794094089779800, 4963086293860560, 31019282772508080, 193870492861908480

Offset

0,2

Comments

Apply the Riordan matrix ((1+sqrt(1-4x))/2,(1-sqrt(1-4x))/2) (inverse of (1/(1-x),x(1-x))) to 5^n.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

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

D-finite with recurrence: 4*n*a(n) = (41*n-24)*a(n-1) - 50*(2*n-3)*a(n-2). - Vaclav Kotesovec, Oct 17 2012

a(n) ~ 3*5^(2*n-1)/4^n. - Vaclav Kotesovec, Oct 17 2012

Mathematica

CoefficientList[Series[(1+Sqrt[1-4*x])/(5*Sqrt[1-4*x]-3), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 17 2012 *)

Prog

(PARI) x='x+O('x^66); Vec((1+sqrt(1-4*x))/(5*sqrt(1-4*x)-3)) \\ Joerg Arndt, May 13 2013

Crossrefs

Cf. A088218, A067336, A076025, A104530, A104532.

Sequence in context: A052609 A077613 A072949 * A225050 A045738 A215708

Adjacent sequences: A104528 A104529 A104530 * A104532 A104533 A104534

Keyword

easy,nonn

Author

Paul Barry, Mar 12 2005

Status

approved