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A090816 a(n) = (3*n+1)!/((2*n)! * n!). 5
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; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = 1/(Integral_{x=0 to 1}(x^2 - x^3)^n dx).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = Sum_{j=0..n} j*binomial(n,j)*binomial(2*n-1,j). - Zerinvary Lajos, Jul 31 2006

EXAMPLE

a(1) = 4!/(2!*1!) = 24/2 = 12.

MAPLE

a:=n->sum(j*binomial(n, j)*binomial(2*n-1, j), j=0..n): seq(a(n), n=1..20); # Zerinvary Lajos, Jul 31 2006

MATHEMATICA

f[n_] := 1/Integrate[(x^2 - x^3)^n, {x, 0, 1}]; Table[ f[n], {n, 0, 19}] (* Robert G. Wilson v, Feb 18 2004 *)

Table[1/Beta[2*n+1, n+1], {n, 0, 20}] (* G. C. Greubel, Feb 03 2019 *)

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 */

(MAGMA) [Factorial(3*n+1)/(Factorial(n)*Factorial(2*n)): n in [0..20]]; // G. C. Greubel, Feb 03 2019

(Sage) [1/beta(2*n+1, n+1) for n in range(20)] # G. C. Greubel, Feb 03 2019

CROSSREFS

Cf. A045721, A002457, A090957, A090969.

Halfdiagonal of triangle A003506.

Sequence in context: A004321 A016223 A027142 * A244722 A144133 A089396

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, Feb 12 2004

STATUS

approved

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Last modified December 4 19:40 EST 2021. Contains 349526 sequences. (Running on oeis4.)