A373660 Triangle read by rows: T(n, k) = (-1)^k*binomial(n, k) * A050446(n, n - k).

1, 2, -1, 6, -6, 1, 30, -42, 15, -1, 190, -340, 186, -32, 1, 1547, -3355, 2460, -700, 65, -1, 15106, -38430, 35295, -14140, 2355, -126, 1, 173502, -506114, 558285, -289520, 71295, -7413, 238, -1, 2286648, -7520040, 9681700, -6174224, 2033920, -328384, 22204, -440, 1

Offset

0,2

Links

Table of n, a(n) for n=0..44.

Guoce Xin and Yueming Zhong, Proving some conjectures on Kekulé numbers for certain benzenoids by using Chebyshev polynomials, arXiv:2201.02376 [math.CO], 2022.

Formula

Row sums are the Euler numbers A000111.

Example

Triangle starts:
  [0]      1;
  [1]      2,      -1;
  [2]      6,      -6,      1;
  [3]     30,     -42,     15,      -1;
  [4]    190,    -340,    186,     -32,     1;
  [5]   1547,   -3355,   2460,    -700,    65,    -1;
  [6]  15106,  -38430,  35295,  -14140,  2355,  -126,   1;
  [7] 173502, -506114, 558285, -289520, 71295, -7413, 238, -1;

Maple

T := (n, k) -> (-1)^k*binomial(n, k) * A050446(n, n - k):
for n from 0 to 7 do print(seq(T(n, k), k=0..n)) od;

Crossrefs

Cf. A050446, A373659 (column 0), A000111 (row sums), A373658 (alternating row sums).

Sequence in context: A008297 A090582 A079641 * A364506 A222864 A232433

Adjacent sequences: A373657 A373658 A373659 * A373661 A373662 A373663

Keyword

sign,tabl

Author

Peter Luschny, Jun 12 2024

Status

approved