A144251 - OEIS

%I #17 Jan 17 2025 14:56:33

%S 1,1,2,6,24,122,758,5606,48378,479532,5390940,68022932,954948752,

%T 14804391270,251815549396,4673137101108,94148342547146,

%U 2050127343000170,48061939075355080,1208742383083994580,32507565146820336836,932149980847656487522,28423646163259392354386,919399182232129554488328

%N Eigensequence of triangle A054142.

%C Eigensequence of the reversed triangle (A085478) = A125273.

%C Eigentriangle A144252 has row sums of A144251 shifted: (1, 2, 6, 24, 122,...) with right border = A144251.

%H Seiichi Manyama, <a href="/A144251/b144251.txt">Table of n, a(n) for n = 0..376</a>

%F a(n) = Sum_{k=0..n-1} A054142(n-1,k)*a(k) for n>0 with a(0)=1.

%e Triangle A054142 begins:

%e   1;

%e   1, 1;

%e   1, 3, 1;

%e   1, 5, 6, 1;

%e   1, 7, 15, 10, 1;

%e   1, 9, 28, 35, 15, 1;

%e   ...

%e a(3) = 6 = 1*1 + 3*1 + 1*2

%e a(4) = 24 = 1*1 + 5*1 + 6*2 + 1*6

%o (PARI) A054142(n, k) = binomial(2*n-k, k);

%o a(n) = if (n==0, 1, sum(k=0, n-1, A054142(n-1,k)*a(k))); \\ too slow

%o 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 Cf. A054142, A085478, A144252,

%K nonn

%O 0,3

%A _Gary W. Adamson_, Sep 16 2008

%E More terms from _Seiichi Manyama_, May 31 2022