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

%I A144252 #9 Jan 18 2025 09:08:13
%S A144252 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,
%T A144252 1680,2562,758,1,13,132,990,5040,15372,21224,5606,1,15,182,1716,11880,
%U A144252 36364,159180,201816,47378,1,17,240,2730,24024,157014,700392,1849980,2177010,479532
%N A144252 Eigentriangle, row sums = A144251 shifted, right border = A144251.
%C A144252 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.
%F A144252 Eigentriangle by rows, T(n,k) = A054142(n,k) * A144251(k); were A144251 = the eigensequence of triangle A054142.
%e A144252 First few rows of the triangle =
%e A144252   1;
%e A144252   1, 1;
%e A144252   1, 3, 2;
%e A144252   1, 5, 12, 6;
%e A144252   1, 7, 30, 60, 24;
%e A144252   1, 9, 56, 210, 360, 122;
%e A144252   1, 11, 90, 504, 1680, 2562, 758;
%e A144252   1, 13, 132, 990, 5040, 15372, 21224, 5606;
%e A144252   ...
%e A144252 The triangle is generated from A054142 and its own eigensequence, A144251.
%e A144252 Triangle A054142 =
%e A144252   1;
%e A144252   1, 1;
%e A144252   1, 3, 1;
%e A144252   1, 5, 6, 1;
%e A144252   1, 7, 15, 10, 1;
%e A144252   ...
%e A144252 The eigensequence of A054142 = A144251: (1, 1, 2, 6, 24, 122, 758, 5606,...);
%e A144252 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).
%o A144252 (PARI) A054142(n, k) = binomial(2*n-k, k);
%o A144252 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;
%o A144252 row(n) = my(v=V144251(n+1)); vector(n+1, k, A054142(n,k-1) * v[k]); \\ _Michel Marcus_, Jan 18 2025
%Y A144252 Cf. A144251, A054142, A125273, A085478
%K A144252 nonn,tabl
%O A144252 0,5
%A A144252 _Gary W. Adamson_, Sep 16 2008
%E A144252 More terms from _Michel Marcus_, Jan 18 2025