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A224340 G.f.: exp( Sum_{n>=1} A113184(n^2)*x^n/n ), where A113184(n) = difference between sum of odd divisors of n and sum of even divisors of n. 3
1, 1, 3, 7, 16, 30, 64, 120, 236, 434, 805, 1445, 2614, 4568, 8003, 13783, 23616, 39886, 67124, 111652, 184862, 303282, 495001, 801939, 1292968, 2070628, 3300796, 5232112, 8256081, 12961543, 20264168, 31535316, 48882592, 75455902, 116041910, 177775284, 271401683 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare to: exp(-Sum_{n>=1} A113184(n)*x^n/n ) = Sum_{n>=1} (-x)^(n*(n+1)/2).

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..1000

FORMULA

Logarithmic derivative yields A224339.

EXAMPLE

L.g.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 16*x^4 + 30*x^5 + 64*x^6 + 120*x^7 +...

where

log(A(x)) = x + 5*x^2/2 + 13*x^3/3 + 29*x^4/4 + 31*x^5/5 + 65*x^6/6 + 57*x^7/7 + 125*x^8/8 + 121*x^9/9 +...+ A113184(n^2)*x^n/n +...

PROG

(PARI) {a(n)=polcoeff(exp(sum(k=1, n, sumdiv(k^2, d, (-1)^d*d)*(-x)^k/k)+x*O(x^n)), n)}

for(n=0, 40, print1(a(n), ", "))

CROSSREFS

Cf. A224339, A113184.

Sequence in context: A213180 A110585 A184677 * A240739 A301117 A000412

Adjacent sequences:  A224337 A224338 A224339 * A224341 A224342 A224343

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 03 2013

STATUS

approved

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Last modified September 27 19:34 EDT 2021. Contains 347694 sequences. (Running on oeis4.)