A356401
a(n) = n! * Sum_{k=1..n} Sum_{d|k} (-1)^(d+1)/(d * (k/d)!).
Original entry on oeis.org
1, 2, 9, 25, 150, 841, 6608, 41945, 437986, 4364741, 51640952, 526219585, 7319856206, 102469338245, 1671439939276, 23909485105217, 427384036676690, 7518024186420421, 149244833247716000, 2756811766466473601, 61545779138627817622, 1354007126970517958885
Offset: 1
-
a(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(d+1)/(d*(k/d)!)));
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, (-1)^k*(exp(x^k)-1)/k)/(1-x)))
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, log(1+x^k)/k!)/(1-x)))
A354505
Expansion of e.g.f. ( Product_{k>0} (1 + x^k)^(1/k!) )^exp(x).
Original entry on oeis.org
1, 1, 3, 13, 54, 291, 1778, 12167, 82869, 655100, 5658257, 51691806, 454932679, 4527660281, 48270581011, 553646849053, 5561424579562, 72988254250439, 1010390962699396, 12295679951427509, 67360732923382327, 1515500302797716376, 45199587363022824107, 1001538050395504921200, -699211952404047871075
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^(1/k!))^exp(x)))
-
a354509(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(d+1)/(d*(k/d)!))/(n-k)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354509(j)*binomial(i-1, j-1)*v[i-j+1])); v;
A356576
Expansion of e.g.f. ( Product_{k>0} (1+x^k)^(1/k!) )^x.
Original entry on oeis.org
1, 0, 2, 0, 24, -55, 630, -2723, 30968, -294327, 3047320, -30255379, 387690732, -5565964391, 77090414492, -1114263777885, 18473122449616, -331776991760303, 6106973926830192, -112710455017397639, 2233663985151902860, -50049383051597936559
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^(1/k!))^x))
-
a352013(n) = (n-1)!*sumdiv(n, d, (-1)^(n/d+1)/(d-1)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*a352013(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;
Showing 1-3 of 3 results.