A120478 Binomial(n+6,5)-binomial(n,5).

6, 21, 56, 126, 252, 461, 786, 1266, 1946, 2877, 4116, 5726, 7776, 10341, 13502, 17346, 21966, 27461, 33936, 41502, 50276, 60381, 71946, 85106, 100002, 116781, 135596, 156606, 179976, 205877, 234486, 265986, 300566, 338421, 379752, 424766

Offset

0,1

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Formula

a(n)=A008488(n+1). [From R. J. Mathar, Aug 07 2008]

a(0)=6, a(1)=21, a(2)=56, a(3)=126, a(4)=252, a(n)=5a(n-1)-10a(n-2)+ 10a(n-3)-5a(n-4)+a(n-5) [From Harvey P. Dale, May 04 2011]

G.f.: (-6 + 9 x - 11 x^2 + 4 x^3 - 2 x^4)/(-1 + x)^5 [From Harvey P. Dale, May 04 2011]

Maple

[seq(binomial(n+6, 5)-binomial(n, 5), n=0..45)];

Mathematica

Table[Binomial[n+6, 5]-Binomial[n, 5], {n, 0, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {6, 21, 56, 126, 252}, 40] (* Harvey P. Dale, May 04 2011 *)

Crossrefs

Sequence in context: A138780 A108907 A306940 * A008488 A023031 A341203

Adjacent sequences: A120475 A120476 A120477 * A120479 A120480 A120481

Keyword

easy,nonn

Author

Zerinvary Lajos, Jul 21 2006

Status

approved