A153344 Limit_{n->oo} A055830^n.

1, 1, 3, 9, 33, 137, 633, 3201, 17525, 102997, 645413, 4288331, 30072815, 221718713, 1712856587, 13825131913, 116289771821, 1017090501489, 9231061705765, 86783120909673, 843731128572093, 8470654690992451, 87697923522936195, 935159181258752679, 10259193455271243201

Offset

0,3

Comments

Powers of the triangle A055830 rapidly converge to a column vector.

Eigensequence of A122075. - Andrew Howroyd, Sep 24 2025

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Prog

(PARI) EigenSeq(nn, tf)={my(v=vector(nn+1)); v[1] = 1; for(n=2, #v, v[n] = sum(k=0, n-2, tf(n-2, k)*v[k+1]); ); v}
seq(nn)={my(M=matrix(nn, nn, n, k, n--; k--; sum(j=0, n-k+1, binomial(n-k-j+1, j)*binomial(n-j, k)))); EigenSeq(nn, (n, k)->M[1+n, 1+k])} \\ Andrew Howroyd, Sep 24 2025

Crossrefs

Cf. A055830, A122075.

Sequence in context: A320187 A207542 A009212 * A193110 A001930 A049425

Adjacent sequences: A153341 A153342 A153343 * A153345 A153346 A153347

Keyword

nonn

Author

Gary W. Adamson, Dec 24 2008

Extensions

a(13) onwards from Andrew Howroyd, Sep 24 2025

Status

approved