A355203 -id:A355203 - cp's OEIS frontend

A355207 E.g.f. A(x) satisfies A'(x) = 1 + 2 * A(1 - exp(-x)).

1, 2, 2, -6, -10, 142, -434, -4478, 88122, -688518, -4032346, 268040678, -5689167298, 53999999466, 1413830543394, -98561802143670, 3282601333608550, -59117973090349066, -1121454296035526786, 171971593399059103618, -10034063428244586340158

Offset: 1

Seiichi Manyama, Jun 24 2022

sign

Seiichi Manyama, Table of n, a(n) for n = 1..329

Cf. A355093, A355203.

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

a(1) = 1; a(n+1) = 2 * Sum_{k=1..n} (-1)^(n-k) * Stirling2(n,k) * a(k).

A355211 E.g.f. A(x) satisfies A'(x) = 1 + A(2 * (1 - exp(-x))).

Original entry on oeis.org

1, 2, 6, 26, 182, 2746, 111350, 11245882, 2521162358, 1193350247226, 1165982253097718, 2322179762944209722, 9356100009656750248822, 75909020176742648718140218, 1236750544861403327611377577974, 40395601774769639548336167153191738

Offset: 1

Seiichi Manyama, Jun 24 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..82

Cf. A355132, A355203, A355207.

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

a(1) = 1; a(n+1) = Sum_{k=1..n} (-1)^(n-k) * 2^k * Stirling2(n,k) * a(k).

cp's OEIS Frontend

A355207 E.g.f. A(x) satisfies A'(x) = 1 + 2 * A(1 - exp(-x)).

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