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A118393 Eigenvector of triangle A059344. E.g.f.: exp( Sum_{n>=0} x^(2^n) ). 2
1, 1, 3, 7, 49, 201, 1411, 7183, 108417, 816049, 9966691, 80843511, 1381416433, 14049020857, 216003063459, 2309595457471, 72927332784001, 1046829280528353, 23403341433961027, 329565129021010279, 9695176730057249841, 160632514329660035881 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

E.g.f. of A059344 is: exp(x+y*x^2). More generally, given a triangle with e.g.f.: exp(x+y*x^b), the eigenvector will have e.g.f.: exp( Sum_{n>=0} x^(b^n) ).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

FORMULA

a(n) = Sum_{k=0..[n/2]} n!/k!/(n-2*k)! *a(k) for n>=0, with a(0)=1.

MAPLE

A118393 := proc(n)

    option remember;

    if n <=1 then

        1;

    else

        n!*add(procname(k)/k!/(n-2*k)!, k=0..n/2) ;

    end if;

end proc:

seq(A118393(n), n=0..20) ; # R. J. Mathar, Aug 19 2014

# second Maple program:

a:= proc(n) option remember; `if`(n=0, 1, add((j-> j!*

      a(n-j)*binomial(n-1, j-1))(2^i), i=0..ilog2(n)))

    end:

seq(a(n), n=0..25);  # Alois P. Heinz, Oct 01 2017

MATHEMATICA

a[0] = 1; a[n_] := a[n] = Sum[n!/k!/(n - 2*k)!*a[k], {k, 0, n/2}];

Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, May 18 2018 *)

PROG

(PARI) a(n)=n!*polcoeff(exp(sum(k=0, #binary(n), x^(2^k))+x*O(x^n)), n)

CROSSREFS

Cf. A059344, variants: A118395, A118930.

Sequence in context: A062959 A275830 A190444 * A113775 A113236 A035499

Adjacent sequences:  A118390 A118391 A118392 * A118394 A118395 A118396

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 07 2006

STATUS

approved

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Last modified March 20 13:18 EDT 2019. Contains 321345 sequences. (Running on oeis4.)