A020928 Expansion of 1/(1-4*x)^(17/2).

1, 34, 646, 9044, 104006, 1040060, 9360540, 77558760, 601080390, 4407922860, 30855460020, 207573094680, 1349225115420, 8510496881880, 52278766560120, 313672599360720, 1842826521244230, 10623352887172620, 60198999693978180, 335847050924299320, 1847158780083646260

Offset

0,2

Links

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

Formula

a(n) = binomial(n+8, 8)*A000984(n+8)/A000984(8), A000984: central binomial coefficients. - Wolfdieter Lang

a(n) = ((2*n+15)*(2*n+13)*(2*n+11)*(2*n+9)*(2*n+7)*(2*n+5)*(2*n+3)*(2*n+1)/2027025)*binomial(2*n, n). - Vincenzo Librandi, Jul 05 2013

Boas-Buck recurrence: a(n) = (34/n)*Sum_{k=0..n-1} 4^(n-k-1)*a(k), n >= 1, a(0) = 1. Proof from a(n) = A046521(n+8, 8). See a comment there. - Wolfdieter Lang, Aug 10 2017

From Amiram Eldar, Mar 27 2022: (Start)

Sum_{n>=0} 1/a(n) = 39708492/1001 - 7290*sqrt(3)*Pi.

Sum_{n>=0} (-1)^n/a(n) = 937500*sqrt(5)*log(phi) - 3029336260/3003, where phi is the golden ratio (A001622). (End)

Mathematica

CoefficientList[Series[1/(1-4x)^(17/2), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 05 2013 *)

Prog

(Magma) [&*[2*n+i: i in [1..15 by 2]]*Binomial(2*n, n)/2027025: n in [0..20]]; // Vincenzo Librandi, Jul 05 2013
(PARI) vector(20, n, n--; m=n+8; binomial(2*m, m)*binomial(m, 8)/12870) \\ G. C. Greubel, Jul 21 2019
(Sage) [binomial(2*(n+8), n+8)*binomial(n+8, 8)/12870 for n in (0..20)] # G. C. Greubel, Jul 21 2019
(GAP) List([0..20], n-> Binomial(2*(n+8), n+8)*Binomial(n+8, 8)/12870); # G. C. Greubel, Jul 21 2019

Crossrefs

Cf. A000984, A001622, A020926, A046521 (ninth column).

Sequence in context: A264067 A004418 A322501 * A061689 A166217 A188711

Adjacent sequences: A020925 A020926 A020927 * A020929 A020930 A020931

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved