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

Author

Gary W. Adamson, Sep 16 2008

Keywords

• nonn

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.

Examples

			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
		

Links

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

Crossrefs

Cf. A054142, A085478, A144252,

Programs

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

Formula

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

Extensions

More terms from Seiichi Manyama, May 31 2022