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A302582 a(n) = n! * [x^n] log(1 + x)/(1 - x)^n. 0
0, 1, 3, 29, 386, 6774, 146484, 3762744, 111868560, 3777096240, 142734788640, 5967788097600, 273488036169600, 13631083378617600, 734083968523046400, 42477063883483622400, 2628184745184816384000, 173147202267665649408000, 12100888735302910523904000, 894183767796064712795136000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

FORMULA

a(n) = n!*Sum_{k=1..n} (-1)^(k+1)*binomial(2*n-k-1,n-k)/k.

a(n) ~ log(3/2) * 2^(2*n - 1/2) * n^n / exp(n). - Vaclav Kotesovec, May 05 2018

MATHEMATICA

Table[n! SeriesCoefficient[Log[1 + x]/(1 - x)^n, {x, 0, n}], {n, 0, 19}]

Table[n! Sum[(-1)^(k + 1) Binomial[2 n - k - 1, n - k]/k, {k, 1,  n}], {n, 0, 19}]

Join[{0}, Table[n^2 (2 (n - 1))! HypergeometricPFQ[{1, 1, 1 - n}, {2, 2 - 2 n}, -1]/n!, {n, 19}]]

CROSSREFS

Cf. A000254, A024167, A058806, A104150, A109792, A300489.

Sequence in context: A081506 A168127 A262640 * A335867 A302923 A326433

Adjacent sequences:  A302579 A302580 A302581 * A302583 A302584 A302585

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 10 2018

STATUS

approved

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Last modified September 28 06:22 EDT 2022. Contains 357063 sequences. (Running on oeis4.)