A144656 a(n) = (n mod 2) if n <= 3, otherwise a(n) = (n^2-5n+7)*(n-2)*a(n-1)/(n-3) + (n^2-5n+7)*a(n-2) - (n-2)*a(n-3)/(n-3).

0, 1, 0, 1, 4, 49, 900, 24649, 944784, 48455521, 3210355600, 267186643801, 27307626948900, 3363915436531441, 491705171699154084, 84158959760104032049, 16675767262618669710400, 3787671541267275818341249, 977702867682508392324162624, 284628954669920840314598014801

Offset: 0

Author

N. J. A. Sloane, Jan 30 2009

Keywords

• nonn

Comments

Terms are squares; square roots give A001053.

References

• M. E. Larsen, Summa Summarum, A. K. Peters, Wellesley, MA, 2007; see p. 35.

Links

• S. B. Ekhad, Problem 10356, Amer. Math. Monthly, 101 (1994), 75.

Crossrefs

Cf. A001053.

Programs

Maple

a:=proc(n) option remember; local m;
if n=0 then RETURN(0); fi;
if n=1 then RETURN(1); fi;
if n=2 then RETURN(0); fi;
if n=3 then RETURN(1); fi;
m:=n-3;
RETURN((m^2+m+1)*(m+1)*a(n-1)/m+(m^2+m+1)*a(n-2)-(m+1)*a(n-3)/m);
end;

PARI

a=vector(10^3); for(n=1, 3, a[n]=n%2); for(n=4, #a, a[n] = (n^2-5*n+7)*(n-2)*a[n-1]/(n-3) + (n^2-5*n+7)*a[n-2] - (n-2)*a[n-3]/(n-3)); concat(0, a) \\ Altug Alkan, Apr 04 2018

Extensions

Typo in name corrected by Rogério Serôdio, Apr 04 2018