A059599 Expansion of (3+x)/(1-x)^6.

3, 19, 69, 189, 434, 882, 1638, 2838, 4653, 7293, 11011, 16107, 22932, 31892, 43452, 58140, 76551, 99351, 127281, 161161, 201894, 250470, 307970, 375570, 454545, 546273, 652239, 774039, 913384, 1072104, 1252152, 1455608, 1684683, 1941723

Offset

0,1

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = binomial(n+4, 4)*(15+4*n)/5.

G.f.: (3+x)/(1-x)^6.

a(-n-4) = -A034263(n). - Bruno Berselli, Aug 23 2011

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Wesley Ivan Hurt, Apr 16 2023

Mathematica

f[n_]:=Binomial[n+4, 4]*(15+4*n)/5; Table[f[n], {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, May 30 2010 *)

Crossrefs

Cf. A034263.

Sequence in context: A158714 A064056 A211061 * A183461 A095662 A090698

Adjacent sequences: A059596 A059597 A059598 * A059600 A059601 A059602

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 02 2001

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, May 30 2010

Status

approved