A190444 E.g.f. exp(x+x^2+x^4).

1, 1, 3, 7, 49, 201, 1411, 7183, 68097, 453169, 4523491, 34273911, 403454833, 3618761017, 45157828899, 445900023871, 6206361667201, 69111310499553, 1017103374816067, 12237616620289639, 195222691795726641, 2575612811875082281, 43240905591424459843, 608870179599833137647

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

E.g.f. exp(x+x^2+x^4).

a(n)=n!*sum(k=1..n, sum(j=floor((4*k-n)/3)..floor((4*k-n)/2), binomial(j,n-4*k+3*j)*binomial(k,j))/k!), n>0, a(0)=1.

D-finite with recurrence a(n) = a(n-1) + 2*(n-1)*a(n-2) + 4*(n-3)*(n-2)*(n-1)*a(n-4). - Vaclav Kotesovec, Oct 09 2013

a(n) ~ 2^(n/2-1) * n^(3*n/4) * exp(n^(1/4)/sqrt(2) - 3*n/4 + sqrt(n)/2 - 1/8) * (1 - 1/(4*sqrt(2)*n^(1/4)) + 43/(192*sqrt(n)) + 271/(768*sqrt(2)*n^(3/4))). - Vaclav Kotesovec, Oct 09 2013

Mathematica

CoefficientList[Series[E^(x+x^2+x^4), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 09 2013 *)

Prog

(Maxima)
a(n):=n!*sum(sum(binomial(j, n-4*k+3*j)*binomial(k, j), j, floor((4*k-n)/3), floor((4*k-n)/2))/k!, k, 1, n);
(PARI)
N=33;  x='x+O('x^N);
egf=exp(x+x^2+x^4);
Vec(serlaplace(egf))
/* Joerg Arndt, Sep 15 2012 */

Crossrefs

Sequence in context: A358593 A062959 A275830 * A118393 A362522 A113775

Adjacent sequences: A190441 A190442 A190443 * A190445 A190446 A190447

Keyword

nonn

Author

Vladimir Kruchinin, May 24 2011

Status

approved