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A337677 a(0) = 1; a(n) = -(n!)^4 * Sum_{k=0..n-1} a(k) / (k! * (n-k))^4. 2
1, -1, 15, -1150, 277760, -164021776, 200693093392, -455136213439776, 1760342776470958080, -10907982472777142353920, 103006437933467240856354816, -1424284967682216438413265543168, 27890228890526992620507064048877568, -752281114397558490715695708227012591616 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..13.

FORMULA

Sum_{n>=0} a(n) * x^n / (n!)^4 = 1 / (1 + polylog(4,x)).

MATHEMATICA

a[0] = 1; a[n_] := a[n] = -(n!)^4 Sum[a[k]/(k! (n - k))^4, {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]

nmax = 13; CoefficientList[Series[1/(1 + PolyLog[4, x]), {x, 0, nmax}], x] Range[0, nmax]!^4

PROG

(PARI) a(n)={n!^4*polcoef(1/(1 + polylog(4, x + O(x*x^n))), n)} \\ Andrew Howroyd, Sep 15 2020

CROSSREFS

Cf. A006252, A074706, A212857, A336260, A337676, A337678.

Sequence in context: A027552 A212857 A266581 * A098210 A090213 A230669

Adjacent sequences:  A337674 A337675 A337676 * A337678 A337679 A337680

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Sep 15 2020

STATUS

approved

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Last modified January 20 19:03 EST 2022. Contains 350472 sequences. (Running on oeis4.)