A367837 Expansion of e.g.f. 1/(2 - x - exp(4*x)).

1, 5, 66, 1294, 33752, 1100504, 43060176, 1965653232, 102548623744, 6018735869824, 392498702352128, 28155539333730560, 2203322337542003712, 186790304541786160128, 17053569926181643921408, 1668166923908523824576512, 174057374767036007615922176

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. A006155, A367835, A367836.

Cf. A285064, A343674, A355112, A367840.

Sequence in context: A297743 A279463 A361409 * A331721 A367847 A209935

Adjacent sequences: A367834 A367835 A367836 * A367838 A367839 A367840

Keyword

nonn

Author

Seiichi Manyama, Dec 02 2023

Status

approved