|
|
A085373
|
|
a(n) = binomial(2n+1, n+1)*binomial(n+2, 2).
|
|
6
|
|
|
1, 9, 60, 350, 1890, 9702, 48048, 231660, 1093950, 5080790, 23279256, 105462084, 473227300, 2106121500, 9307051200, 40873466520, 178520875830, 775924068150, 3357800061000, 14473885526100, 62168784497820, 266168518910580
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n-1) = Sum_{1<=i1<=i2<=...<=in<=n} (i1 + i2 + ... + in).
G.f.: (1 - x)/(1 - 4*x)^(5/2). (End)
Sum_{n>=0} 1/a(n) = 4*Pi^2/9 - 4*Pi/sqrt(3) + 4.
Sum_{n>=0} (-1)^n/a(n) = 8*sqrt(5)*log(phi) - 16*log(phi)^2 - 4, where phi = A001622 is the golden ratio. (End)
|
|
MATHEMATICA
|
Table[Binomial[2n+1, n+1]Binomial[n+2, 2], {n, 0, 30}]
|
|
PROG
|
(PARI) a(n)=binomial(2*n+1, n+1)*binomial(n+2, 2)
(Magma) [Binomial(2*n+1, n+1)*Binomial(n+2, 2): n in [0..30]]; // G. C. Greubel, Feb 12 2019
(Sage) [binomial(2*n+1, n+1)*binomial(n+2, 2) for n in (0..30)] # G. C. Greubel, Feb 12 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Mario Catalani (mario.catalani(AT)unito.it), Jun 26 2003
|
|
STATUS
|
approved
|
|
|
|