A367831 E.g.f. A(x) satisfies A(x) = (1 + (exp(x) - 1) * A(3*x)) / (1 - x).

1, 2, 17, 529, 60191, 24822701, 36413854321, 186201636968159, 3260017071214457747, 192544750449664642891369, 37901471231124512743264725077, 24619109083914012570141331273785011, 52334858943702505364559907161989713988743

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 3^(n-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, 3^(i-j)*binomial(i, j)*v[i-j+1])); v;

Crossrefs

Cf. A006155, A367830.

Cf. A367836.

Sequence in context: A217284 A220476 A293178 * A367829 A172341 A356502

Adjacent sequences: A367828 A367829 A367830 * A367832 A367833 A367834

Keyword

nonn

Author

Seiichi Manyama, Dec 02 2023

Status

approved