

A027659


Binomial(n+2,2)+binomial(n+3,3)+binomial(n+4,4)+binomial(n+5,5).


5



4, 18, 52, 121, 246, 455, 784, 1278, 1992, 2992, 4356, 6175, 8554, 11613, 15488, 20332, 26316, 33630, 42484, 53109, 65758, 80707, 98256, 118730, 142480, 169884, 201348, 237307, 278226, 324601
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6, 15, 20, 15, 6, 1).


FORMULA

G.f.: (x^2)*(2x)*(22*x+x^2)/(1x)^6. (For numerator polynomial see N5(5, x)= 46*x+4*x^2x^3 from A063422.)
C(5+n,5)C(1+n,1)  Zerinvary Lajos, May 08 2006
a(0)=4, a(1)=18, a(2)=52, a(3)=121, a(4)=246, a(5)=455, a(n)=6*a(n1) 15*a(n2)+20*a(n3)15*a(n4)+6*a(n5)a(n6).  Harvey P. Dale, Aug 18 2012


MAPLE

1/120*(n+8)*(n+2)*(n+1)*(n^2+9*n+30);


MATHEMATICA

Table[Sum[Binomial[n+i, i], {i, 2, 5}], {n, 0, 30}] (* or *) LinearRecurrence[ {6, 15, 20, 15, 6, 1}, {4, 18, 52, 121, 246, 455}, 30] (* Harvey P. Dale, Aug 18 2012 *)


PROG

(PARI) a(n)=(n+8)*(n+2)*(n+1)*(n^2+9*n+30)/120 \\ Charles R Greathouse IV, Oct 07 2015


CROSSREFS

a(n)= A035343(n+2, 5), n >= 0 (sixth column of quintinomial coefficients).
a(n)= A062750(n+2, 5), n >= 0 (sixth column).
Sequence in context: A256430 A225263 A092349 * A059133 A300493 A300876
Adjacent sequences: A027656 A027657 A027658 * A027660 A027661 A027662


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane.


STATUS

approved



