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A118395 E.g.f.: exp(x + x^3). 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Equals row sums of triangle A118394.

LINKS

Robert Israel, Table of n, a(n) for n = 0..533

FORMULA

E.g.f.: 1 + x/(1+x)*(G(0) - 1) where G(k) =  1 + (1+x^2)/(k+1)/(1-x/(x+(1)/G(k+1) )), recursively defined continued fraction. - Sergei N. Gladkovskii, Feb 04 2013

a(n) ~ 3^(n/3-1/2) * n^(2*n/3) * exp((n/3)^(1/3)-2*n/3). - Vaclav Kotesovec, Jun 02 2013

E.g.f.: A(x) = exp(x+x^3) satisfies A' - (1+3*x^2)*A = 0. - Gheorghe Coserea, Aug 24 2015

a(n+1) = a(n) + 3*n*(n-1)*a(n-2). - Gheorghe Coserea, Aug 24 2015

MAPLE

with(combstruct):seq(count(([S, {S=Set(Union(Z, Prod(Z, Z, Z)))}, labeled], size=n)), n=1..22); # Zerinvary Lajos, Mar 18 2008

MATHEMATICA

CoefficientList[Series[E^(x+x^3), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 02 2013 *)

PROG

(PARI) a(n)=n!*polcoeff(exp(x+x^3+x*O(x^n)), n)

(PARI)

N=33;  x='x+O('x^N);

egf=exp(x+x^3);

Vec(serlaplace(egf))

/* Joerg Arndt, Sep 15 2012 */

(MAGMA) [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

CROSSREFS

Cf. A118394, A118396.

Sequence in context: A098538 A033814 A321165 * A118396 A193375 A185787

Adjacent sequences:  A118392 A118393 A118394 * A118396 A118397 A118398

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 07 2006

EXTENSIONS

Missing a(0)=1 prepended by Joerg Arndt, Sep 15 2012

STATUS

approved

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Last modified March 18 22:07 EDT 2019. Contains 321305 sequences. (Running on oeis4.)