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A261254 Coefficients in an asymptotic expansion of A261239 in falling factorials. 7
1, -4, 2, -4, -21, -136, -996, -8152, -73811, -733244, -7938186, -93126716, -1178054657, -15998857056, -232339375664, -3594982133808, -59070662442383, -1027605845674036, -18873206761567638, -365015243426704372, -7416392564276075453, -157957992952546414328 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..446

FORMULA

a(n) ~ -4 * n! * (1 - 5/n + 5/n^2 - 30/n^4 - 286/n^5 - 2960/n^6 - 34890/n^7 - 459705/n^8 - 6678641/n^9 - 105999991/n^10).

For n>0, a(n) = Sum_{k=1..n} A261253(k) * Stirling1(n-1, k-1).

EXAMPLE

A261239(n)/(-3*n!) ~ 1 - 4/n + 2/(n*(n-1)) - 4/(n*(n-1)*(n-2)) - 21/(n*(n-1)*(n-2)*(n-3)) - 136/(n*(n-1)*(n-2)*(n-3)*(n-4)) - 996/(n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)) - ... [coefficients are A261254]

A261239(n)/(-3*n!) ~ 1 - 4/n + 2/n^2 - 2/n^3 - 31/n^4 - 288/n^5 - 2939/n^6 - ... [coefficients are A261253]

MATHEMATICA

CoefficientList[Assuming[Element[x, Reals], Series[E^(4/x) * x^4 / ExpIntegralEi[1/x]^4, {x, 0, 25}]], x]

CROSSREFS

Cf. A003319, A260503, A259472, A261214, A261239, A261253.

Sequence in context: A302603 A085689 A134434 * A168613 A248251 A139809

Adjacent sequences:  A261251 A261252 A261253 * A261255 A261256 A261257

KEYWORD

sign

AUTHOR

Vaclav Kotesovec, Aug 12 2015

STATUS

approved

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Last modified March 18 16:00 EDT 2019. Contains 321292 sequences. (Running on oeis4.)