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
Examples
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).
Programs
-
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
Formula
Extensions
More terms from Michel Marcus, Jan 18 2025
Comments