A261239 Coefficients in an asymptotic expansion of A259472 in falling factorials.

1, -3, 0, -4, -21, -129, -910, -7242, -64155, -626319, -6685548, -77527104, -971315713, -13084909917, -188723009274, -2902997766470, -47458671376503, -821951603042523, -15037432614035864, -289828080356525052, -5870642802374608509, -124691017072423632777

Offset: 0

Author

Vaclav Kotesovec, Aug 12 2015

Keywords

• sign

Examples

			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]
		

Links

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

Crossrefs

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

Programs

Mathematica

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

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).