A354507
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) * d )/(k * (n-k)!).
Original entry on oeis.org
1, 3, 14, 48, 269, 1615, 12662, 73528, 836817, 8476243, 99348534, 948849176, 13193115597, 177346261391, 3684976294222, 45021819481808, 734808219625345, 13524660020400771, 290452222949307070, 4639956700466396256, 128621330002689008237, 2735863084773695212719
Offset: 1
-
a(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1)*d)/(k*(n-k)!));
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, (-x)^k/(k*(1-x^k)))))
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=1, N, log(1+x^k))))
A354508
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) * d^2 )/(k * (n-k)!).
Original entry on oeis.org
1, 5, 32, 168, 1189, 8785, 77384, 646296, 7306737, 79997893, 1005481784, 12518370128, 184109233125, 2671256865121, 47934480000112, 754158322407248, 13813898274148737, 262680987222463269, 5518034466415262320, 107988236156057411096, 2605128008760639636677
Offset: 1
-
a(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1)*d^2)/(k*(n-k)!));
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, (-x)^k/(k*(1-x^k)^2))))
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=1, N, k*log(1+x^k))))
A354503
Expansion of e.g.f. ( Product_{k>0} (1 + x^k)^(1/k) )^exp(x).
Original entry on oeis.org
1, 1, 3, 14, 67, 424, 3093, 26060, 233917, 2427224, 27565317, 339002146, 4450167269, 63343680802, 964189902141, 15769859929260, 270255218753593, 4913097747513800, 94513145955643993, 1904990351069631390, 40153307898034641361, 893402292594225679438
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^(1/k))^exp(x)))
-
a354506(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1))/(k*(n-k)!));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354506(j)*binomial(i-1, j-1)*v[i-j+1])); v;
Showing 1-3 of 3 results.