A033464 Logarithmic (or "LOG") transform of squares A000290.

1, 3, -1, -26, 29, 756, -1793, -45744, 189513, 4700260, -30515629, -730341600, 6948349069, 159130156836, -2123506814505, -46081244842304, 838034409016721, 17029766318842692, -414549408916313189, -7774211453384941440, 251026027696302116181, 4263756050277024153028

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..435

Crossrefs

Cf. A000290, A033462.

Programs

Maple

logtr:= proc(p) local b; b:= proc(n) option remember; if n=0 then 1 else p(n)- add(k *binomial(n,k) *p(n-k) *b(k), k=1..n-1)/n fi end; n->b(n+1) end: a:= logtr(n-> n^2): seq(a(n), n=0..25); # Alois P. Heinz, Sep 14 2008

Mathematica

With[{nn=30},CoefficientList[Series[(Exp[x](1+3x+x^2))/(1+Exp[x]x(1+x)),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 03 2019 *)

Formula

E.g.f.: exp(x)*(1 + 3*x + x^2)/(1 + exp(x)*x*(1 + x)). - Ilya Gutkovskiy, Mar 06 2018