A302610
Expansion of e.g.f. -log(1 - x)*arcsinh(x).
Original entry on oeis.org
0, 0, 2, 3, 4, 20, 158, 819, 3624, 33984, 427482, 3819915, 29665260, 404822340, 6948032310, 88407058635, 991515848400, 17715286764000, 383952670412850, 6349179054589875, 93532380775766100, 2063197602667372500, 53913667654307868750, 1098018631195048591875
Offset: 0
-log(1 - x)*arcsinh(x) = 2*x^2/2! + 3*x^3/3! + 4*x^4/4! + 20*x^5/5! + 158*x^6/6! + 819*x^7/7! + 3624*x^8/8! + ...
Cf.
A009410,
A009416,
A009429,
A009435,
A012572,
A104150,
A177699,
A177700,
A296435,
A296727,
A302611.
-
a:=series(-log(1-x)*arcsinh(x),x=0,24): seq(n!*coeff(a,x,n),n=0..23); # Paolo P. Lava, Mar 26 2019
-
nmax = 23; CoefficientList[Series[-Log[1 - x] ArcSinh[x], {x, 0, nmax}], x] Range[0, nmax]!
A302611
Expansion of e.g.f. -log(1 - x)*arctanh(x).
Original entry on oeis.org
0, 0, 2, 3, 16, 50, 368, 1764, 16896, 109584, 1297152, 10628640, 149944320, 1486442880, 24349317120, 283465647360, 5287713177600, 70734282393600, 1480103564083200, 22376988058521600, 519000166327910400, 8752948036761600000, 222845873874075648000, 4148476779335454720000
Offset: 0
-log(1 - x)*arctanh(x) = 2*x^2/2! + 3*x^3/3! + 16*x^4/4! + 50*x^5/5! + 368*x^6/6! + 1764*x^7/7! + 16896*x^8/8! + ...
Cf.
A005359,
A009410,
A009416,
A009429,
A009435,
A012697,
A081358,
A104150,
A177699,
A177700,
A202139,
A302610.
-
a:=series(-log(1-x)*arctanh(x),x=0,24): seq(n!*coeff(a,x,n),n=0..23); # Paolo P. Lava, Mar 26 2019
-
nmax = 23; CoefficientList[Series[-Log[1 - x] ArcTanh[x], {x, 0, nmax}], x] Range[0, nmax]!
-
x='x+O('x^99); concat([0, 0], Vec(serlaplace(log(1-x)*log((1-x)/(1+x))/2))) \\ Altug Alkan, Apr 10 2018
A351882
Expansion of e.g.f. 1 / (1 - x)^sec(x).
Original entry on oeis.org
1, 1, 2, 9, 42, 255, 1785, 14406, 131236, 1328037, 14809965, 180014054, 2371072374, 33607312219, 510183508471, 8255546409722, 141855645636152, 2579236008913689, 49471832899923129, 998261936044450726, 21138674688880283370, 468687157358947546415, 10858634384569444410179
Offset: 0
-
nmax = 22; CoefficientList[Series[1/(1 - x)^Sec[x], {x, 0, nmax}], x] Range[0, nmax]!
-
my(x='x+O('x^30)); Vec(serlaplace(1/(1-x)^(1/cos(x)))) \\ Michel Marcus, Feb 23 2022
A347072
E.g.f.: -log(1 - x) * (sec(x) + tan(x)).
Original entry on oeis.org
0, 1, 3, 8, 28, 119, 605, 3597, 24624, 191481, 1672273, 16240509, 173870156, 2036293453, 25910852669, 356057435177, 5255621683776, 82932788545297, 1393129225943169, 24819194946609589, 467369450831456492, 9274872837974110805, 193447045984755732413
Offset: 0
-
nmax = 22; CoefficientList[Series[-Log[1 - x] (Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := If[n == 0, 0, (n - 1)!]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Table[a[n], {n, 0, 22}]
-
from itertools import accumulate, count, islice
def A347072_gen(): # generator of terms
blist, m = (0,), 1
yield from blist
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist),initial=m)))[-1]
m *= i
A347072_list = list(islice(A347072_gen(),40)) # Chai Wah Wu, Jun 12 2022
Showing 1-4 of 4 results.
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