A367835 Expansion of e.g.f. 1/(2 - x - exp(2*x)).

1, 3, 22, 242, 3544, 64872, 1424976, 36517840, 1069533824, 35240047232, 1290137297152, 51955085596416, 2282489348834304, 108630445541684224, 5567741266098944000, 305752314499878569984, 17909736027185859100672, 1114647522476340562132992

Offset: 0

Author

Seiichi Manyama, Dec 02 2023

Keywords

• nonn

Crossrefs

Cf. A006155, A367836, A367837.

Cf. A126390, A216794, A343672, A355110, A367838.

Programs

Maple

A367835 := proc(n)
    option remember ;
    if n = 0 then
        1 ;
    else
        n*procname(n-1)+add(2^k*binomial(n,k)*procname(n-k),k=1..n) ;
    end if;
end proc:
seq(A367835(n),n=0..70) ; # R. J. Mathar, Dec 04 2023

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 2^j*binomial(i, j)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 2^k * binomial(n,k) * a(n-k).