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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)*(2-x)*(2-2*x+x^2)/(1-x)^6. (For numerator polynomial see N5(5, x)= 4-6*x+4*x^2-x^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(n-1)- 15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - 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

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)