A105943 a(n) = C(n+7,n) * C(n+10,7).

120, 2640, 28512, 205920, 1132560, 5096520, 19631040, 66745536, 204787440, 576438720, 1507608960, 3700494720, 8593371072, 19004570640, 40244973120, 81980500800, 161264274600, 307350735120, 569168028000, 1026681084000, 1807851474000, 3113521983000

Offset

0,1

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Formula

G.f.: (24*(-5*x^4-35*x^3-63*x^2-35*x-5))/(x-1)^15. - Harvey P. Dale, Nov 14 2011

From Amiram Eldar, Sep 06 2022: (Start)

Sum_{n>=0} 1/a(n) = 114905939/6480 - 5390*Pi^2/3.

Sum_{n>=0} (-1)^n/a(n) = 14336*log(2)/9 - 3577279/3240. (End)

Example

If n=0 then C(0+7,0)*C(0+10,7) = C(7,0)*C(10,7) = 1*120 = 120.
If n=6 then C(6+7,6)*C(6+10,7) = C(13,6)*C(16,7) = 1716*11440 = 19631040.

Maple

A105943:=n->binomial(n+7, n)*binomial(n+10, 7): seq(A105943(n), n=0..40); # Wesley Ivan Hurt, Apr 18 2017

Mathematica

Table[Binomial[n+7, n]Binomial[n+10, 7], {n, 0, 30}] (* Harvey P. Dale, Nov 14 2011 *)

Prog

(Python)
A105943_list, m = [], [3432, -3432, 1320, 0]+[120]*11
for _ in range(10**2):
    A105943_list.append(m[-1])
    for i in range(14):
        m[i+1] += m[i] # Chai Wah Wu, Jan 24 2016

Crossrefs

Cf. A062145.

Sequence in context: A032180 A000553 A126232 * A219945 A219834 A250651

Adjacent sequences: A105940 A105941 A105942 * A105944 A105945 A105946

Keyword

easy,nonn

Author

Zerinvary Lajos, Apr 27 2005

Extensions

More terms from Harvey P. Dale, Nov 14 2011

Status

approved