A072372 a(0) = 1, a(1) = 1, a(n) = 2*a(n-1) + (2*n-1)^2*a(n-2) for n > 1.

1, 1, 11, 47, 633, 5073, 86739, 1030815, 21577905, 341061345, 8471746395, 167351545935, 4816256934825, 114227230079025, 3739505765645475, 103544112027750975, 3800753264840803425, 120361044527902418625, 4896644838485789032875, 174567559635669989163375

Offset: 0

Author

N. J. A. Sloane, Jul 19 2002

Keywords

• nonn

References

• A. E. Jolliffe, Continued Fractions, in Encyclopaedia Britannica, 11th ed., pp. 30-33; see p. 31.

Crossrefs

Cf. A024199, A024200.

Programs

Maple

f := proc(n) local a, b, t1, t2, t3, i, j, k; option remember; a := 1; b := 1; if n = 0 then RETURN(a); elif n = 1 then RETURN(b); else RETURN(2*f(n - 1) + (2*n - 1)^2*f(n - 2)); fi; end: seq(f(n), n=0..20); # adapted to offset 0 by Georg Fischer, Dec 23 2019

Mathematica

RecurrenceTable[{a[0]==a[1]==1, a[n]==2*a[n-1] + (2n-1)^2*a[n-2]}, a, {n,0,20}]
(* Harvey P. Dale, Nov 15 2018, adapted to offset 0 by Georg Fischer, Dec 23 2019 *)

Extensions

Definition adapted to offset 0 by Georg Fischer, Dec 23 2019