A165489 Eigensequence of triangle A084938.

1, 1, 1, 2, 6, 23, 105, 550, 3236, 21127, 152084, 1204107, 10484455, 100487135, 1060590050, 12312607512, 156705050156, 2175091977023, 32715771430649, 529684212426756, 9173124311640887, 168981073675685354, 3295492196522826838, 67770145132669795948, 1464690528426085313858

Offset

0,4

Comments

Triangle A084938 * [1, 1, 1, 2, 6, 23, 105, 550,...] shifts left to [1, 1, 2, 6, 23, 105, 550,...].

Eigentriangle A165490 = A084938 * its eigensequence, A165489 as a diagonalized infinite lower triangular matrix.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Formula

The sequence can be obtained by shifting down triangle A084938 one row, then inserting a "1" as the first term, obtaining a new triangle Q. Then take the Lim_{n->inf.} Q^n, obtaining a shifted left column vector [1, 1, 1, 2, 6, 23, 105, 550, 3236,...].

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}
T084938(n)={my(v=vector(n+1)); v[1] = [1]; for(n=1, n, v[1+n]=vector(1+n, k, k--; if(k>0, sum(j=0, n-k, j!*v[n-j][k])))); v}
seq(nn) = { my(T=T084938(nn-1)); EigenSeq(nn, (n, k)->T[1+n][1+k]) } \\ Andrew Howroyd, Sep 23 2025

Crossrefs

Cf. A084938, A165490.

Sequence in context: A080108 A113227 A200406 * A352367 A192315 A381718

Adjacent sequences: A165486 A165487 A165488 * A165490 A165491 A165492

Keyword

eigen,nonn

Author

Gary W. Adamson, Sep 20 2009

Extensions

a(0)=1 prepended and a(11) onwards from Andrew Howroyd, Sep 23 2025

Status

approved