A144251 Eigensequence of triangle A054142.

1, 1, 2, 6, 24, 122, 758, 5606, 48378, 479532, 5390940, 68022932, 954948752, 14804391270, 251815549396, 4673137101108, 94148342547146, 2050127343000170, 48061939075355080, 1208742383083994580, 32507565146820336836, 932149980847656487522, 28423646163259392354386, 919399182232129554488328

Offset

0,3

Comments

Eigensequence of the reversed triangle (A085478) = A125273.

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

Links

Seiichi Manyama, Table of n, a(n) for n = 0..376

Formula

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

Example

Triangle A054142 begins:
  1;
  1, 1;
  1, 3, 1;
  1, 5, 6, 1;
  1, 7, 15, 10, 1;
  1, 9, 28, 35, 15, 1;
  ...
a(3) = 6 = 1*1 + 3*1 + 1*2
a(4) = 24 = 1*1 + 5*1 + 6*2 + 1*6

Prog

(PARI) A054142(n, k) = binomial(2*n-k, k);
a(n) = if (n==0, 1, sum(k=0, n-1, A054142(n-1, k)*a(k))); \\ too slow
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

Crossrefs

Cf. A054142, A085478, A144252,

Sequence in context: A144167 A104983 A375458 * A304198 A243806 A201158

Adjacent sequences: A144248 A144249 A144250 * A144252 A144253 A144254

Keyword

nonn,changed

Author

Gary W. Adamson, Sep 16 2008

Extensions

More terms from Seiichi Manyama, May 31 2022

Status

approved