|
| |
|
|
A090816
|
|
a(n)=(3n+1)!/((2n)!n!).
|
|
2
| |
|
|
1, 12, 105, 840, 6435, 48048, 352716, 2558160, 18386775, 131231100, 931395465, 6580248480, 46312074900, 324897017760, 2272989850440, 15863901576864, 110487596768703, 768095592509700, 5330949171823275, 36945070220658600
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| a(n)=1/(integral_{x=0 to 1}(x^2-x^3)^n dx).
|
|
|
FORMULA
| a:=n->sum(j*binomial(n,j)*binomial(2*n-1,j),j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 31 2006
|
|
|
EXAMPLE
| E.g. a(3)=840.
|
|
|
MAPLE
| a:=n->sum(j*binomial(n, j)*binomial(2*n-1, j), j=0..n): seq(a(n), n=1..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 31 2006
|
|
|
MATHEMATICA
| f[n_] := 1/Integrate[(x^2 - x^3)^n, {x, 0, 1}]; Table[ f[n], {n, 0, 19}] (from Robert G. Wilson v Feb 18 2004)
|
|
|
PROG
| (PARI) a(n)=if(n<0, 0, (3*n+1)!/(2*n)!/n!) - Michael Somos Feb 14 2004
(PARI) a(n)=if(n<0, 0, 1/subst(intformal((x^2-x^3)^n), x, 1)) - Michael Somos Feb 14 2004
|
|
|
CROSSREFS
| Cf. A045721.
Halfdiagonal of triangle A003506.
Sequence in context: A004321 A016223 A027142 * A144133 A089396 A166755
Adjacent sequences: A090813 A090814 A090815 * A090817 A090818 A090819
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Al Hakanson (hawkuu(AT)excite.com), Feb 11 2004
|
|
|
EXTENSIONS
| New definition from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 12 2004
|
| |
|
|
