A367840 Expansion of e.g.f. 1/(2 + x - exp(4*x)).

1, 3, 34, 514, 10456, 265704, 8103120, 288302480, 11722944896, 536262671488, 27256865214208, 1523936708699904, 92949383868668928, 6141694449341637632, 437033351625771001856, 33319937543640487708672, 2709708041047388536274944

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(0) = 1; a(n) = -n * a(n-1) + Sum_{k=1..n} 4^k * binomial(n,k) * a(n-k).

Prog

(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, 4^j*binomial(i, j)*v[i-j+1])); v;

Crossrefs

Cf. A032032, A367838, A367839.

Cf. A367786, A367837.

Sequence in context: A134491 A045727 A105713 * A337388 A317653 A143638

Adjacent sequences: A367837 A367838 A367839 * A367841 A367842 A367843

Keyword

nonn

Author

Seiichi Manyama, Dec 02 2023

Status

approved