0,3

Term-by-term square of sequence with e.g.f.: exp(x+m/2*x^2) is given by e.g.f.: exp(x/(1-m*x))/sqrt(1-m^2*x^2) for all m.

Combinatorial interpretation: a(n) counts the partitions of a set of n distinguishable objects into subsets of size 1 and 2 with the additional feature that the constituents of the subset of size 2 acquire 2 colors. - K. A. Penson and P. Blasiak (penson(AT)lptl.jussieu.fr; blasiak(AT)lptl.jussieu.fr), Jun 03 2006

In general, e.g.f. exp(x+m*x^2) has general term sum{k=0..n, C(n,k)*m^k*(n-k)!/(n-m*k)!}. [From Paul Barry (pbarry(AT)wit.ie), Nov 07 2008]

Term-by-term square equals A115330 which has e.g.f.: exp(x/(1-4*x))/sqrt(1-16*x^2).

a(n)=sum{k=0..floor(n/2), C(n-k,k)2^k*n!/(n-k)!}=sum{k=0..n, C(n,k)2^k*(n-k)!/(n-2k)!}. [From Paul Barry (pbarry(AT)wit.ie), Nov 07 2008]

(PARI) a(n)=local(m=4); n!*polcoeff(exp(x+m/2*x^2+x*O(x^n)), n)

Cf. A115330.

Sequence in context: A075063 A100209 A139361 this_sequence A137702 A140120 A064169

Adjacent sequences: A115326 A115327 A115328 this_sequence A115330 A115331 A115332

nonn,new

Paul D. Hanna (pauldhanna(AT)juno.com), Jan 20 2006

More terms from K. A. Penson and P. Blasiak (penson(AT)lptl.jussieu.fr; blasiak(AT)lptl.jussieu.fr), Jun 03 2006