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A306948 Expansion of e.g.f. (1 + x)*log(1 + x)*exp(x). 0
0, 1, 3, 5, 8, 9, 19, -15, 216, -1407, 11803, -108483, 1106192, -12363703, 150381243, -1977666743, 27965386320, -423158076351, 6822782712723, -116781368777867, 2114916140765496, -40404117909336247, 812091479233464131, -17130720178674680031, 378423227774537955688 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..24.

FORMULA

a(n) = Sum_{k=0..n} Stirling1(n,k)*A000110(k)*k.

a(n) = Sum_{k=1..n} (-1)^(k-1)*binomial(n,k)*(n - k + 1)*(k - 1)!.

a(n) ~ exp(-1) * (-1)^n * n! / n^2. - Vaclav Kotesovec, Mar 18 2019

MAPLE

a:=series((1 + x)*log(1 + x)*exp(x), x=0, 25): seq(n!*coeff(a, x, n), n=0..24); # Paolo P. Lava, Mar 26 2019

MATHEMATICA

nmax = 24; CoefficientList[Series[(1 + x) Log[1 + x] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!

Table[Sum[StirlingS1[n, k] BellB[k] k, {k, 0, n}], {n, 0, 24}]

Table[Sum[(-1)^(k - 1) Binomial[n, k] (n - k + 1) (k - 1)!, {k, 1, n}], {n, 0, 24}]

CROSSREFS

Cf. A000110, A002741, A048994, A070071, A216313.

Sequence in context: A018804 A032682 A022769 * A067241 A120943 A087792

Adjacent sequences:  A306945 A306946 A306947 * A306949 A306950 A306951

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Mar 17 2019

STATUS

approved

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Last modified October 27 08:46 EDT 2020. Contains 338035 sequences. (Running on oeis4.)