A367972 -id:A367972 - cp's OEIS frontend

A367971 Expansion of e.g.f. exp(exp(-x) - 1)/(1 - x).

1, 0, 2, 1, 19, 43, 461, 2350, 22940, 185313, 1969105, 20981585, 255992617, 3300259584, 46394533498, 694535043925, 11123040844947, 189008829494295, 3402841007703469, 64648146404160854, 1293014652241452452, 27152832827254344741, 597366828915334031625

Offset: 0

Seiichi Manyama, Dec 06 2023

nonn

Cf. A101053, A367972.

Cf. A000110, A087650, A186755.

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

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

a(n) = n! * Sum_{k=0..n} (-1)^k * Bell(k)/k!, where Bell() is A000110.

A367973 Expansion of e.g.f. exp(exp(x) - 1)/(1 - 2*x).

Original entry on oeis.org

1, 3, 14, 89, 727, 7322, 88067, 1233815, 19745180, 355434387, 7108803715, 156394360300, 3753468860797, 97590218025159, 2732526295603774, 81975790251071765, 2623225298514438627, 89189660232355783122

Offset: 0

Seiichi Manyama, Dec 06 2023

Cf. A000110, A367972.

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

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

a(n) = n! * Sum_{k=0..n} 2^(n-k) * Bell(k)/k!, where Bell() is A000110.

cp's OEIS Frontend

A367971 Expansion of e.g.f. exp(exp(-x) - 1)/(1 - x).

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