A355097 -id:A355097 - cp's OEIS frontend

A355096 E.g.f. A(x) satisfies A(x) = 1 + 2 * log(1+x) * A(log(1+x)).

1, 2, 6, 16, -12, -492, 628, 63488, -408112, -20183928, 444216616, 9449212584, -679737200176, 2572902869080, 1276955484043864, -53294396490490656, -1891642613896659904, 314259171327032640928, -8590801196259162852288, -1381246455381881103425424

Offset: 0

Seiichi Manyama, Jun 19 2022

sign

Cf. A354728, A355097.

Cf. A355104.

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

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

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

A355105 E.g.f. A(x) satisfies A(x) = 1 + 3 * x * A(log(1+x)).

Original entry on oeis.org

1, 3, 18, 135, 1044, 6210, -5994, -760347, -3009960, 261689616, 1960394400, -220644396522, -1043258760828, 366570209524896, -3109452797977470, -972076070389224105, 36160406771040130320, 3274635904971823559880, -331428842765036684941320

Offset: 0

Seiichi Manyama, Jun 19 2022

sign

Cf. A354729, A355104.

Cf. A355097.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=3*i*sum(j=0, i-1, stirling(i-1, j, 1)*v[j+1])); v;

a(0) = 1; a(n) = 3 * n * Sum_{k=0..n-1} Stirling1(n-1,k) * a(k).

a(n) = 3 * n * A355097(n-1) for n>0.

cp's OEIS Frontend

A355096 E.g.f. A(x) satisfies A(x) = 1 + 2 * log(1+x) * A(log(1+x)).

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