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A144251 Eigensequence of triangle A054142.

%I A144251 #17 Jan 17 2025 14:56:33
%S A144251 1,1,2,6,24,122,758,5606,48378,479532,5390940,68022932,954948752,
%T A144251 14804391270,251815549396,4673137101108,94148342547146,
%U A144251 2050127343000170,48061939075355080,1208742383083994580,32507565146820336836,932149980847656487522,28423646163259392354386,919399182232129554488328
%N A144251 Eigensequence of triangle A054142.
%C A144251 Eigensequence of the reversed triangle (A085478) = A125273.
%C A144251 Eigentriangle A144252 has row sums of A144251 shifted: (1, 2, 6, 24, 122,...) with right border = A144251.
%H A144251 Seiichi Manyama, <a href="/A144251/b144251.txt">Table of n, a(n) for n = 0..376</a>
%F A144251 a(n) = Sum_{k=0..n-1} A054142(n-1,k)*a(k) for n>0 with a(0)=1.
%e A144251 Triangle A054142 begins:
%e A144251   1;
%e A144251   1, 1;
%e A144251   1, 3, 1;
%e A144251   1, 5, 6, 1;
%e A144251   1, 7, 15, 10, 1;
%e A144251   1, 9, 28, 35, 15, 1;
%e A144251   ...
%e A144251 a(3) = 6 = 1*1 + 3*1 + 1*2
%e A144251 a(4) = 24 = 1*1 + 5*1 + 6*2 + 1*6
%o A144251 (PARI) A054142(n, k) = binomial(2*n-k, k);
%o A144251 a(n) = if (n==0, 1, sum(k=0, n-1, A054142(n-1,k)*a(k))); \\ too slow
%o A144251 lista(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; \\ _Michel Marcus_, Jan 17 2025
%Y A144251 Cf. A054142, A085478, A144252,
%K A144251 nonn
%O A144251 0,3
%A A144251 _Gary W. Adamson_, Sep 16 2008
%E A144251 More terms from _Seiichi Manyama_, May 31 2022