A355105 -id:A355105 - cp's OEIS frontend

A355104 E.g.f. A(x) satisfies A(x) = 1 + 2 * x * A(log(1+x)).

1, 2, 8, 36, 128, -120, -5904, 8792, 1015808, -7346016, -403678560, 9772765552, 226781102016, -17673167204576, 72041280334240, 38308664521315920, -1705420687695700992, -64315848872486436736, 11313330167773175073408, -326450445457848188386944

Offset: 0

Seiichi Manyama, Jun 19 2022

sign

Cf. A354729, A355105.

Cf. A355096.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=2*i*sum(j=0, i-1, stirling(i-1, j, 1)*v[j+1])); v;

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

a(n) = 2 * n * A355096(n-1) for n>0.

A355097 E.g.f. A(x) satisfies A(x) = 1 + 3 * log(1+x) * A(log(1+x)).

Original entry on oeis.org

1, 3, 15, 87, 414, -333, -36207, -125415, 9692208, 65346480, -6686193834, -28979410023, 9399236141664, -74034590428035, -21601690453093869, 753341807730002715, 64208547156310265880, -6137571162315494165580, -131200755856066508312736

Offset: 0

Seiichi Manyama, Jun 19 2022

sign

Cf. A354728, A355096.

Cf. A355105.

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

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

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

cp's OEIS Frontend

A355104 E.g.f. A(x) satisfies A(x) = 1 + 2 * x * A(log(1+x)).

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