OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
From David Callan, Nov 20 2003: (Start)
a(n-1) = Sum_{1<=i1<=i2<=...<=in<=n} (i1 + i2 + ... + in).
G.f.: (1 - x)/(1 - 4*x)^(5/2). (End)
a(n) = A119578(n+1)/2. - Zerinvary Lajos, Jun 19 2008
From Amiram Eldar, May 14 2022: (Start)
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