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A261239 Coefficients in an asymptotic expansion of A259472 in falling factorials. 7
1, -3, 0, -4, -21, -129, -910, -7242, -64155, -626319, -6685548, -77527104, -971315713, -13084909917, -188723009274, -2902997766470, -47458671376503, -821951603042523, -15037432614035864, -289828080356525052, -5870642802374608509, -124691017072423632777 (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) ~ -3 * n! * (1 - 4/n + 2/n^2 - 2/n^3 - 31/n^4 - 288/n^5 - 2939/n^6 - 33944/n^7 - 438614/n^8 - 6266312/n^9 - 98050303/n^10), coefficients are A261253.

For n>0, a(n) = Sum_{k=1..n} A261214(k) * Stirling1(n-1, k-1).

EXAMPLE

A259472(n)/(-2*n!) ~ 1 - 3/n - 4/(n*(n-1)*(n-2)) - 21/(n*(n-1)*(n-2)*(n-3)) - 129/(n*(n-1)*(n-2)*(n-3)*(n-4)) - ... [coefficients are A261239]

A259472(n)/(-2*n!) ~ 1 - 3/n - 4/n^3 - 33/n^4 - 283/n^5 - 2785/n^6 - ... [coefficients are A261214]

MATHEMATICA

CoefficientList[Assuming[Element[x, Reals], Series[E^(3/x) * x^3 / ExpIntegralEi[1/x]^3, {x, 0, 25}]], x]

CROSSREFS

Cf. A003319, A260503, A259472, A261214, A261253, A261254.

Sequence in context: A094665 A309053 A052439 * A261214 A143073 A154725

Adjacent sequences: A261236 A261237 A261238 * A261240 A261241 A261242

KEYWORD

sign

AUTHOR

Vaclav Kotesovec, Aug 12 2015

STATUS

approved

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Last modified December 7 15:01 EST 2022. Contains 358667 sequences. (Running on oeis4.)