A007744 Expansion of (1+6*x)/(1-4*x)^(7/2).

1, 20, 210, 1680, 11550, 72072, 420420, 2333760, 12471030, 64664600, 327202876, 1622493600, 7909656300, 38003792400, 180324117000, 846321189120, 3934071152550, 18132120329400, 82937661506700, 376780512108000, 1701164012167620, 7637879238303600, 34117964696719800

Offset

0,2

Comments

Fourth column in A104684. - Paul Barry, May 02 2005

Diagonal of the rational function 1 / (1 - x - y)^4. - Ilya Gutkovskiy, Apr 23 2025

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Ömür Deveci and Anthony G. Shannon, Some aspects of Neyman triangles and Delannoy arrays, Mathematica Montisnigri, Vol. L (2021), 36-43.

Aleksandar Petojević and Nenad Đapić, The vAm(a,b,c;z) function, Preprint, 2013.

Georg Thimm, Emails to N. J. A. Sloane, Sep. 1994.

Formula

a(n) = binomial(2n+3, n) * binomial(n+3, 3). - Paul Barry, May 02 2005

G.f.: G(0) where G(k) = 1 + 4*x*(k+1)*(4*k+5)/((2*k+1)^2 - x*(2*k+1)^2*(2*k+3)*(4*k+7)/(x*(2*k+3)*(4*k+7) + 2*(k+1)^2/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jul 12 2012

D-finite with recurrence: n*a(n) + 2*(n-11)*a(n-1) + 12*(-2*n-1)*a(n-2) = 0. - R. J. Mathar, Nov 24 2012

a(n) ~ 4^(n+1) * n^(5/2) / (3 * sqrt(Pi)). - Amiram Eldar, Sep 22 2025

Mathematica

Array[Binomial[2 # + 3, #]*Binomial[# + 3, 3] &, 19, 0] (* Michael De Vlieger, Aug 18 2021 *)

Prog

(Magma) [Binomial(2*n+3, n)*Binomial(n+3, 3): n in [0..20]]; // Vincenzo Librandi, Aug 20 2011

Crossrefs

Cf. A104684.

Sequence in context: A126905 A341236 A022585 * A353892 A353881 A304023

Adjacent sequences: A007741 A007742 A007743 * A007745 A007746 A007747

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved