A118396
Eigenvector of triangle A118394; E.g.f.: exp( Sum_{n>=0} x^(3^n) ).
Original entry on oeis.org
1, 1, 1, 7, 25, 61, 481, 2731, 10417, 454105, 4309921, 23452111, 592433161, 6789801877, 46254009985, 893881991731, 11548704851041, 93501748795441, 4828847934591937, 83867376656907415, 823025819684123641, 33409213329178701421, 640457721676922946721
Offset: 0
-
a:= proc(n) option remember; `if`(n=0, 1, add((j-> j!*
a(n-j)*binomial(n-1, j-1))(3^i), i=0..ilog[3](n)))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Oct 01 2017
-
a[n_] := a[n] = If[n==0, 1, Sum[Function[j, j! a[n-j] Binomial[n-1, j-1]][3^i], {i, 0, Log[3, n]}]];
a /@ Range[0, 25] (* Jean-François Alcover, Nov 07 2020, after Alois P. Heinz *)
-
{a(n)=n!*polcoeff(exp(sum(k=0,ceil(log(n+1)/log(3)),x^(3^k))+x*O(x^n)),n)}
A118395
Expansion of e.g.f. exp(x + x^3).
Original entry on oeis.org
1, 1, 1, 7, 25, 61, 481, 2731, 10417, 91225, 681121, 3493711, 33597961, 303321877, 1938378625, 20282865331, 211375647841, 1607008257841, 18157826367937, 212200671085975, 1860991143630841, 22560913203079021, 289933758771407521, 2869267483843753147, 37116733726117707025
Offset: 0
-
[n le 3 select 1 else Self(n-1) + 3*(n-2)*(n-3)*Self(n-3): n in [1..26]]; // Vincenzo Librandi, Aug 25 2015
-
with(combstruct):seq(count(([S, {S=Set(Union(Z, Prod(Z, Z, Z)))}, labeled], size=n)), n=0..22); # Zerinvary Lajos, Mar 18 2008
-
CoefficientList[Series[E^(x+x^3), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 02 2013 *)
T[n_, k_] := n!/(k!(n-3k)!);
a[n_] := Sum[T[n, k], {k, 0, Floor[n/3]}];
a /@ Range[0, 24] (* Jean-François Alcover, Nov 04 2020 *)
-
a(n)=n!*polcoeff(exp(x+x^3+x*O(x^n)),n)
-
N=33; x='x+O('x^N);
egf=exp(x+x^3);
Vec(serlaplace(egf))
/* Joerg Arndt, Sep 15 2012 */
-
a(n) = n!*sum(k=0, n\3, binomial(n-2*k, k)/(n-2*k)!); \\ Seiichi Manyama, Feb 25 2022
-
def a(n):
if (n<3): return 1
else: return a(n-1) + 3*(n-1)*(n-2)*a(n-3)
[a(n) for n in (0..25)] # G. C. Greubel, Feb 18 2021
Showing 1-2 of 2 results.
Comments