login
A356039
a(n) = Sum_{k=1..n} binomial(n,k) * sigma_3(k).
1
1, 11, 58, 243, 866, 2804, 8485, 24387, 67333, 180086, 469338, 1196976, 2996956, 7385837, 17954243, 43125267, 102494548, 241309031, 563341508, 1305142418, 3002938045, 6866090880, 15609292379, 35299794600, 79443050541, 177989130174, 397124963671, 882642816697, 1954708794400
OFFSET
1,2
COMMENTS
For m>0, Sum_{k=1..n} binomial(n,k) * sigma_m(k) ~ zeta(m+1) * n^m * 2^(n-m).
LINKS
Eric Weisstein's World of Mathematics, Divisor Function.
FORMULA
a(n) ~ Pi^4 * n^3 * 2^(n-4) / 45.
a(n) = Sum_{i=1..n} Sum_{j=1..n} (i^3)*binomial(n,i*j). - Ridouane Oudra, Oct 31 2022
MAPLE
with(numtheory): seq(add(sigma[3](i)*binomial(n, i), i=1..n), n=1..60); # Ridouane Oudra, Oct 31 2022
MATHEMATICA
Table[Sum[Binomial[n, k] * DivisorSigma[3, k], {k, 1, n}], {n, 1, 40}]
PROG
(PARI) a(n) = sum(k=1, n, binomial(n, k) * sigma(k, 3)); \\ Michel Marcus, Jul 24 2022
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 24 2022
STATUS
approved