A367836 Expansion of e.g.f. 1/(2 - x - exp(3*x)).

1, 4, 41, 627, 12759, 324543, 9906453, 352785933, 14358074211, 657405969075, 33444798498657, 1871613674744553, 114259520317835871, 7556674046930376111, 538212358684663414317, 41071433946325564954581, 3343141735414440335583003

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} 3^k * binomial(n,k) * a(n-k).

Mathematica

With[{nn=20}, CoefficientList[Series[1/(2-x-Exp[3x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Feb 16 2024 *)

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

Crossrefs

Cf. A006155, A367835, A367837.

Cf. A284859, A343673, A355111.

Sequence in context: A085340 A230251 A001908 * A367846 A270703 A363302

Adjacent sequences: A367833 A367834 A367835 * A367837 A367838 A367839

Keyword

nonn

Author

Seiichi Manyama, Dec 02 2023

Status

approved