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A206764 a(n) = Sum_{k=1..n} binomial(n,k) * sigma(n,k) * (-1)^(n-k). 1
1, -1, 10, 79, 1026, 15686, 279938, 5771359, 134218243, 3487832974, 100000000002, 3138673052878, 106993205379074, 3937454749863382, 155568096631586820, 6568441588686506943, 295147905179352825858, 14063102470280932000757, 708235345355337676357634 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Here sigma(n,k) equals the sum of the k-th powers of the divisors of n.

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

L.g.f.: L(x) = x - x^2/2 + 10*x^3/3 + 79*x^4/4 + 1026*x^5/5 + 15686*x^6/6 +...

Exponentiation yields the g.f. of A206763:

exp(L(x) = 1 + x + 3*x^3 + 23*x^4 + 225*x^5 + 2824*x^6 + 42670*x^7 +...

Illustration of terms.

a(2) = -2*sigma(2,1) + 1*sigma(2,2) = -2*3 + 1*5 = -1;

a(3) = 3*sigma(3,1) - 3*sigma(3,2) + 1*sigma(3,3) = 3*4 - 3*10 + 1*28 = 10;

a(4) = -4*sigma(4,1) + 6*sigma(4,2) - 4*sigma(4,3) + 1*sigma(4,4) = -4*7 + 6*21 - 4*73 + 1*273 = 79.

PROG

(PARI) {a(n)=sum(k=1, n, binomial(n, k)*sigma(n, k)*(-1)^(n-k))}

(PARI) {a(n)=n*polcoeff(sum(k=1, n, (1/k)*log((1-(-x)^k)/(1-(k-1)^k*x^k +x*O(x^n)))), n)}

for(n=1, 21, print1(a(n), ", "))

CROSSREFS

Cf. A206763 (exp), A205815, A205812.

Sequence in context: A077245 A036732 A251309 * A253649 A244729 A027790

Adjacent sequences:  A206761 A206762 A206763 * A206765 A206766 A206767

KEYWORD

sign

AUTHOR

Paul D. Hanna, Feb 12 2012

STATUS

approved

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Last modified November 22 18:55 EST 2019. Contains 329410 sequences. (Running on oeis4.)