A243633 Expansion of (4*x^3-6*x^2+4*x-1)/(5*x^3-8*x^2+5*x-1).

1, 1, 3, 8, 21, 56, 152, 417, 1149, 3169, 8738, 24083, 66356, 182806, 503597, 1387317, 3821839, 10528644, 29005093, 79905508, 220130016, 606431481, 1670644817, 4602422317, 12679110454, 34929397819, 96226217048, 265091454958, 730294527501, 2011872083081, 5542461470187

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Formula

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

G.f.: 1/(1-F(x)), where F(x) is g.f. A038504.

Prog

(Maxima)
a(n):=sum(sum(binomial(m+k-1, k)*binomial(n+m-1, n-4*k-m), k, 0, n/2), m, 0, n);

Crossrefs

Cf. A038504.

Sequence in context: A128105 A085560 A318900 * A094374 A008909 A006835

Adjacent sequences: A243630 A243631 A243632 * A243634 A243635 A243636

Keyword

nonn,easy

Author

Vladimir Kruchinin, Jun 08 2014

Extensions

More terms from Jason Yuen, Dec 28 2025

Status

approved