A356406
a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d * (k/d)^d).
Original entry on oeis.org
1, 4, 16, 79, 443, 2968, 22216, 189698, 1792402, 18745036, 213452996, 2653142952, 35448861576, 509724975264, 7824794618208, 128006170541328, 2217950478978576, 40686737647774368, 785852762719168992, 15974195890305405696, 340376906088298319616
Offset: 1
-
a(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)^d)));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-x^k/k))/(1-x)))
A356409
Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k!) )^(1/(1-x)).
Original entry on oeis.org
1, 1, 5, 28, 203, 1756, 17802, 205010, 2644287, 37669096, 586855058, 9914829508, 180429770402, 3516313661706, 73029591042943, 1609531482261375, 37504691293842367, 920966310015565936, 23764054962685200642, 642681497080268685092, 18174504398294667649782
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, 1-x^k/k!)^(1/(1-x))))
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a356407(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!^d)));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356407(j)*binomial(i-1, j-1)*v[i-j+1])); v;
A354341
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} 1/(d * ((k/d)!)^d) )/(n-k)!.
Original entry on oeis.org
1, 4, 12, 38, 130, 557, 2877, 18314, 136458, 1180457, 11389081, 122833207, 1446973931, 18594740348, 257507754524, 3835059283282, 60937544854850, 1030871972064485, 18469079943443229, 349656695460113159, 6969526853682012755, 145958486484692023936
Offset: 1
-
a182926(n) = n!*sumdiv(n, d, 1/(d*(n/d)!^d));
a(n) = sum(k=1, n, a182926(k)*binomial(n, k));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, log(1-x^k/k!))))
Showing 1-3 of 3 results.