A354506
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) )/(k * (n-k)!).
Original entry on oeis.org
1, 2, 7, 14, 63, 284, 2385, 3940, 87717, 940126, 12743267, 30055618, 562302323, 9005878920, 423435780989, 2080544097000, 24457758561001, 444510436079706, 17533073308723423, 46973556239255702, 7501223613055891783, 178483805340054632084, 4396051786608296882889, -31788150263554644516724
Offset: 1
-
a(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1))/(k*(n-k)!));
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=1, N, log(1+x^k)/k)))
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))))
A354504
Expansion of e.g.f. ( Product_{k>0} (1 + x^k)^k )^exp(x).
Original entry on oeis.org
1, 1, 6, 48, 402, 4375, 54595, 777189, 12284188, 215999025, 4132338673, 85640640877, 1910121348674, 45571124446445, 1157169377895739, 31150000798832647, 885481496002286200, 26498034473000080321, 832407848080194500301, 27378188500890922864153
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^k)^exp(x)))
-
a354508(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1)*d^2)/(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, a354508(j)*binomial(i-1, j-1)*v[i-j+1])); v;
Showing 1-3 of 3 results.