A172385 a(n) = 1 if n=0, otherwise Sum_{k=0..floor((n-1)/2)} binomial(n-k-1, k) *(-1)^k*a(n-1-2k).

1, 1, 1, 0, -2, -4, -1, 14, 34, 2, -189, -439, 263, 3796, 6997, -14437, -96643, -106774, 671097, 2800836, 57519, -31088662, -82674287, 155322877, 1455331563, 1936970102, -14267868745, -66446614533, 19215003803, 1037638182571, 2654391633166, -8675836955120, -67833031653088

Offset: 0

Author

Paul Barry, Feb 01 2010

Keywords

• easy
• sign

Examples

			Eigensequence for the number triangle
   1;
   1,   0;
   0,   1,   0;
  -1,   0,   1,   0;
   0,  -2,   0,   1,   0;
   1,   0,  -3,   0,   1,   0;
   0,   3,   0,  -4,   0,   1,   0;
  -1,   0,   6,   0,  -5,   0,   1,   0;
   0,  -4,   0,  10,   0,  -6,   0,   1,   0;
   1,   0, -10,   0,  15,   0,  -7,   0,   1,   0;
   0,   5,   0, -20,   0,  21,   0,  -8,   0,   1,   0;
(augmented version of Riordan array (1/(1+x^2), x/(1+x^2)).
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..949

Crossrefs

Cf. A172383, A360898, A360899.

Programs

Mathematica

a[n_] := If[n == 0, 1, Sum[Binomial[n - k - 1, k]*(-1)^k*a[n - 2*k - 1], {k, 0, Floor[(n - 1)/2]}]]; Table[a[n], {n, 0, 30}] (* G. C. Greubel, Oct 07 2018 *)

Formula

G.f.: A(x) = 1 + (x/(1+x^2))*A(x/(1+x^2)).

Extensions

Name corrected by G. C. Greubel, Oct 07 2018

Terms a(27) and beyond from Seiichi Manyama, Feb 25 2023