OFFSET
0,3
COMMENTS
Numerators in expansion of sqrt(1/sqrt(1-4x)). - Paul Barry, Jul 12 2005
Denominators are in A088802. - Michael Somos, Aug 23 2007
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = prod(k=1, n, (4k-3)/k * 2^A007814(k)), proved by Mitch Harris, following a conjecture by Ralf Stephan.
a(n) = 2^(e_2((2n)!)-n)/n! Product[4k+1,{k,0,n-1}], where e_2((2n)!) is the highest power of 2 that divides (2n)! (sequence A005187). - Emanuele Munarini, Jan 25 2011
Numerators in (1-4t)^(-1/4) = 1 + t + (5/2)t^2 + (15/2)t^3 + (195/8)t^4 + (663/8)t^5 + (4641/16)t^6 + (16575/16)t^7 + ... = 1 + t + 5*t^2/2! + 45*t^3/3! + 585*t^4/4! + ... = e.g.f. for the quartic factorials A007696 (cf. A094638). - Tom Copeland, Dec 04 2013
MATHEMATICA
Table[Numerator[Binomial[-1/4, n] (-1)^n], {n, 0, 20}]
PROG
(PARI) {a(n) = if( n<0, 0, numerator( polcoeff( (1 - x +x*O(x^n))^(-1/4), n ) ) ) } /* Michael Somos, Aug 23 2007 */
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
STATUS
approved