%I A090816
%S A090816 1,12,105,840,6435,48048,352716,2558160,18386775,131231100,931395465,
%T A090816 6580248480,46312074900,324897017760,2272989850440,15863901576864,
%U A090816 110487596768703,768095592509700,5330949171823275,36945070220658600
%N A090816 a(n)=(3n+1)!/((2n)!n!).
%C A090816 a(n)=1/(integral_{x=0 to 1}(x^2-x^3)^n dx).
%F A090816 a:=n->sum(j*binomial(n,j)*binomial(2*n-1,j),j=0..n). - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jul 31 2006
%e A090816 E.g. a(3)=840.
%p A090816 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
%t A090816 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)
%o A090816 (PARI) a(n)=if(n<0,0,(3*n+1)!/(2*n)!/n!) - Michael Somos Feb 14 2004
%o A090816 (PARI) a(n)=if(n<0,0,1/subst(intformal((x^2-x^3)^n),x,1)) - Michael Somos 
               Feb 14 2004
%Y A090816 Cf. A045721.
%Y A090816 Halfdiagonal of triangle A003506.
%Y A090816 Sequence in context: A004321 A016223 A027142 this_sequence A144133 A089396 
               A166755
%Y A090816 Adjacent sequences: A090813 A090814 A090815 this_sequence A090817 A090818 
               A090819
%K A090816 nonn,easy
%O A090816 0,2
%A A090816 Al Hakanson (hawkuu(AT)excite.com), Feb 11 2004
%E A090816 New definition from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 12 2004