A379781 a(1)=1, a(2)=2; thereafter, a(n) is the final value at the bottom of the difference triangle of the sequence thus far.

1, 2, 1, -2, 0, 7, -14, -12, 155, -408, -364, 7693, -30940, 10712, 637701, -4224222, 9980180, 61922567, -810337234, 4100137008, -958593005, -174952472228, 1662063951016, -6944673371867, -22887336602200, 655644589917172, -5694691183524699, 19946666531550638, 176993602416669640

Offset

1,2

Comments

The difference triangle refers to the triangular array of iterated differences.

The first term in each row of the difference triangle is the inverse binomial transform of the sequence, so the definition means the inverse binomial transform deletes term a(2) = 2.

Links

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..595

Example

To find a(6), we look at the first difference triangle of the first 5 terms:
  1,   2,   1,  -2,   0
  1,  -1,  -3,   2
 -2,  -2,   5
  0,   7
  7
7 is the final value, so a(6)=7.

Mathematica

a[1] = 1; a[2] = 2; a[n_] := a[n] = Sum[(-1)^(n-k+1) * Binomial[n-2, k-1] * a[k], {k, 1, n-1}]; Table[a[n], {n, 1, 30}] (* Amiram Eldar, Jan 04 2025 *)

Crossrefs

Cf. A014182, A010739.

Sequence in context: A327359 A197522 A121310 * A356919 A278158 A218880

Adjacent sequences: A379778 A379779 A379780 * A379782 A379783 A379784

Keyword

sign

Author

Neal Gersh Tolunsky, Jan 02 2025

Status

approved