A105947 a(n) = C(n+6,n)*C(n+4,4).

1, 35, 420, 2940, 14700, 58212, 194040, 566280, 1486485, 3578575, 8016008, 16893240, 33786480, 64574160, 118605600, 210327264, 361499985, 604167795, 984569740, 1568220500, 2446423980, 3744526500, 5632263000, 8336601000, 12157543125, 17487410031, 24834191760

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

G.f.: (15*x^4+80*x^3+90*x^2+24*x+1) / (1-x)^11. [Colin Barker, Jan 28 2013]

From Wesley Ivan Hurt, Jan 27 2022: (Start)

a(n) = (17280 + 78336*n + 152376*n^2 + 167780*n^3 + 116150*n^4 + 52983*n^5 +

16173*n^6 + 3270*n^7 + 420*n^8 + 31*n^9 + n^10)/17280.

a(n) = 11*a(n-1)-55*a(n-2)+165*a(n-3)-330*a(n-4)+462*a(n-5)-462*a(n-6)+330*a(n-7)-165*a(n-8)+55*a(n-9)-11*a(n-10)+a(n-11). (End)

From Amiram Eldar, Sep 08 2022: (Start)

Sum_{n>=0} 1/a(n) = 224*Pi^2 - 55244/25.

Sum_{n>=0} (-1)^n/a(n) = 12*Pi^2 + 512*log(2)/5 - 4711/25. (End)

Example

If n=0 then C(0+6,0)*C(0+4,4) = C(6,0)*C(4,4) = 1*1 = 1.
If n=10 then C(10+6,10)*C(10+4,4) = C(16,10)*C(14,4) = 8008*1001 = 8016008.

Mathematica

Table[Binomial[n+6, n]Binomial[n+4, 4], {n, 0, 30}] (* or *) LinearRecurrence[ {11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {1, 35, 420, 2940, 14700, 58212, 194040, 566280, 1486485, 3578575, 8016008}, 30] (* Harvey P. Dale, May 21 2014 *)

Crossrefs

Cf. A062196.

Sequence in context: A075664 A133317 A322879 * A183846 A219936 A298946

Adjacent sequences: A105944 A105945 A105946 * A105948 A105949 A105950

Keyword

easy,nonn

Author

Zerinvary Lajos, Apr 27 2005

Extensions

Terms from a(8) onwards corrected by Colin Barker, Jan 28 2013

Second example corrected by Colin Barker, Jan 28 2013

Status

approved