A355084 -id:A355084 - cp's OEIS frontend

A355085 E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(3*x).

1, 1, 5, 128, 13572, 5462934, 7948602294, 40533916402440, 709019302729063320, 41863690463023189162224, 8239820880700969013925719856, 5352039696398504114334881521575792, 11377141201027327036487229661596883688304

Offset: 0

Seiichi Manyama, Jun 18 2022

nonn

Cf. A006252, A355084.

Cf. A355087, A355088.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (-1)^(j-1)*3^(i-j)*(j-1)!*binomial(i, j)*v[i-j+1])); v;

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * 3^(n-k) * (k-1)! * binomial(n,k) * a(n-k).

A355120 E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(2 * log(1+x)).

Original entry on oeis.org

1, 1, 3, 26, 654, 45084, 7934924, 3381663872, 3365978050576, 7632454575648720, 38732162420625498608, 434139952882119137261024, 10640704036253473615712677216, 565765176687479152385624223741568, 64834956096893473256448986077914291328

Offset: 0

Seiichi Manyama, Jun 20 2022

nonn

Cf. A354728, A355084, A355096, A355133.

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

E.g.f. A(x) satisfies: A(exp(x) - 1) = 1 + x*A(2*x).

a(0) = 1; a(n) = Sum_{k=1..n} k * 2^(k-1) * Stirling1(n,k) * a(k-1).

cp's OEIS Frontend

A355085 E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(3*x).

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