A355103 -id:A355103 - cp's OEIS frontend

A355102 E.g.f. A(x) satisfies A(x) = 1 + 2 * x * A(1 - exp(-x)).

1, 2, 8, 36, 112, -500, -10056, 24220, 2184480, -8762868, -1076904200, 13388615108, 954279034416, -32517111227484, -1095519424670888, 104108720480963940, 63376017498217152, -394143964914859213828, 17135457626785509446184, 1359360091138085321022956

Offset: 0

Seiichi Manyama, Jun 19 2022

sign

Cf. A354574, A355103.

Cf. A355093.

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, (-1)^(i-j-1)*stirling(i-1, j, 2)*v[j+1])); v;

a(0) = 1; a(n) = 2 * n * Sum_{k=0..n-1} (-1)^(n-k-1) * Stirling2(n-1,k) * a(k).

a(n) = 2 * n * A355093(n-1) for n>0.

A355094 E.g.f. A(x) satisfies A(x) = 1 + 3 * (1 - exp(-x)) * A(1 - exp(-x)).

Original entry on oeis.org

1, 3, 15, 84, 321, -2157, -57126, -23496, 19229199, 114026754, -14369595177, -124727102772, 21679898019936, 89714147328354, -57010454409251982, 653678598376462566, 223463102168891738085, -9691395708350731626375, -1087655068021435814109648

Offset: 0

Seiichi Manyama, Jun 19 2022

sign

Cf. A353177, A355093.

Cf. A355103.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=3*sum(j=1, i, (-1)^(i-j)*j*stirling(i, j, 2)*v[j])); v;

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

a(0) = 1; a(n) = 3 * Sum_{k=1..n} (-1)^(n-k) * k * Stirling2(n,k) * a(k-1).

cp's OEIS Frontend

A355102 E.g.f. A(x) satisfies A(x) = 1 + 2 * x * A(1 - exp(-x)).

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