A144252 Eigentriangle, row sums = A144251 shifted, right border = A144251.

1, 1, 1, 1, 3, 2, 1, 5, 12, 6, 1, 7, 30, 60, 24, 1, 9, 56, 210, 360, 122, 1, 11, 90, 504, 1680, 2562, 758, 1, 13, 132, 990, 5040, 15372, 21224, 5606, 1, 15, 182, 1716, 11880, 36364, 159180, 201816, 47378, 1, 17, 240, 2730, 24024, 157014, 700392, 1849980, 2177010, 479532

Offset

0,5

Comments

Right border = A144251: (1, 1, 2, 6, 24, 122, 758,...) with row sums = the same sequence shifted. Sum of n-th row terms = rightmost term of next row.

Links

Table of n, a(n) for n=0..54.

Formula

Eigentriangle by rows, T(n,k) = A054142(n,k) * A144251(k); were A144251 = the eigensequence of triangle A054142.

Example

First few rows of the triangle =
  1;
  1, 1;
  1, 3, 2;
  1, 5, 12, 6;
  1, 7, 30, 60, 24;
  1, 9, 56, 210, 360, 122;
  1, 11, 90, 504, 1680, 2562, 758;
  1, 13, 132, 990, 5040, 15372, 21224, 5606;
  ...
The triangle is generated from A054142 and its own eigensequence, A144251.
Triangle A054142 =
  1;
  1, 1;
  1, 3, 1;
  1, 5, 6, 1;
  1, 7, 15, 10, 1;
  ...
The eigensequence of A054142 = A144251: (1, 1, 2, 6, 24, 122, 758, 5606,...);
Example: row 3 of A144252 = (1, 5, 12, 6) = termwise products of (1, 5, 6, 1) and (1, 1, 2, 6) = (1*1, 5*1, 6*2, 1*6).

Prog

(PARI) A054142(n, k) = binomial(2*n-k, k);
V144251(nn) = my(v=vector(nn)); v[1] = 1; for (n=2, nn, v[n] = sum(k=0, n-1, A054142(n-2, k)*v[k+1]); ); v;
row(n) = my(v=V144251(n+1)); vector(n+1, k, A054142(n, k-1) * v[k]); \\ Michel Marcus, Jan 18 2025

Crossrefs

Cf. A144251, A054142, A125273, A085478

Sequence in context: A085792 A108123 A105954 * A248033 A318254 A002130

Adjacent sequences: A144249 A144250 A144251 * A144253 A144254 A144255

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 16 2008

Extensions

More terms from Michel Marcus, Jan 18 2025

Status

approved