A261254
Coefficients in an asymptotic expansion of A261239 in falling factorials.
Original entry on oeis.org
1, -4, 2, -4, -21, -136, -996, -8152, -73811, -733244, -7938186, -93126716, -1178054657, -15998857056, -232339375664, -3594982133808, -59070662442383, -1027605845674036, -18873206761567638, -365015243426704372, -7416392564276075453, -157957992952546414328
Offset: 0
A261239(n)/(-3*n!) ~ 1 - 4/n + 2/(n*(n-1)) - 4/(n*(n-1)*(n-2)) - 21/(n*(n-1)*(n-2)*(n-3)) - 136/(n*(n-1)*(n-2)*(n-3)*(n-4)) - 996/(n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)) - ... [coefficients are A261254]
A261239(n)/(-3*n!) ~ 1 - 4/n + 2/n^2 - 2/n^3 - 31/n^4 - 288/n^5 - 2939/n^6 - ... [coefficients are A261253]
-
CoefficientList[Assuming[Element[x, Reals], Series[E^(4/x) * x^4 / ExpIntegralEi[1/x]^4, {x, 0, 25}]], x]
Original entry on oeis.org
0, 0, 1, 2, 7, 32, 177, 1142, 8411, 69692, 642581, 6534978, 72754927, 880877928, 11530686953, 162331760494, 2446380427331, 39300220067668, 670480457586813, 12106985274788506, 230691361507912471, 4625811718758963136
Offset: 0
G.f. = x^2 + 2*x^3 + 7*x^4 + 32*x^5 + 177*x^6 + 1142*x^7 + 8411*x^8 + ...
- L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 262 (#14).
-
a[0]=0; a[n_]:=a[n] = n!-Sum[k!*a[n-k], {k,1,n-1}]; Table[Sum[a[k]*a[n-k],{k,0,n}],{n,0,20}] (* Vaclav Kotesovec, Aug 03 2015 *)
CoefficientList[Assuming[Element[x, Reals], Series[(1 - x*E^(1/x) / ExpIntegralEi[1/x])^2, {x, 0, 20}]], x] (* Vaclav Kotesovec, Aug 03 2015 *)
A356291
Number of reducible permutations.
Original entry on oeis.org
0, 0, 1, 3, 11, 49, 259, 1593, 11227, 89537, 799475, 7917897, 86257643, 1025959345, 13234866787, 184078090137, 2746061570587, 43736283267137, 740674930879379, 13289235961616937, 251805086618856395, 5024288943352588369, 105295629327037117123
Offset: 0
-
A356291 := n -> n! - A003319(n): seq(A356291(n), n = 0..22);
-
def A356291_list(size: int):
F, R, C = 1, [0], [1] + [0] * (size - 1)
for n in range(1, size):
F *= n
for k in range(n, 0, -1):
C[k] = C[k - 1] * k
C[0] = -sum(C[k] for k in range(1, n + 1))
R.append(F + C[0])
return R
print(A356291_list(23))
# The test predicate, not suitable for calculation:
def reducible(p) -> bool:
return any(i for i in range(0, len(p))
if all(p[j] < p[k]
for j in range(0, i)
for k in range(i, len(p))
))
from itertools import permutations
for n in range(8): print(len([p for p in permutations(range(n)) if reducible(p)]))
A260913
Coefficients in asymptotic expansion of sequence A059439.
Original entry on oeis.org
1, -1, -1, 1, 30, 404, 5379, 76021, 1155805, 18931873, 333434490, 6295452542, 127007655461, 2729179670279, 62275740709651, 1504740573206497, 38398859322225738, 1032354879165190692, 29174916098556605939, 864859538577015162053, 26840211278794388530737
Offset: 0
A059439(n)/(2*(n-1)!) ~ 1 - 1/n - 1/n^2 + 1/n^3 + 30/n^4 + 404/n^5 + 5379/n^6 + ...
A305275
Coefficients in asymptotic expansion of sequence A302557.
Original entry on oeis.org
1, 0, 2, 6, 35, 256, 2187, 21620, 243947, 3098528, 43799819, 682540780, 11630529643, 215190967544, 4296657514283, 92083313483300, 2108244638675035, 51350077108834832, 1325682930813985547, 36157047428501464220, 1038793351537388253211, 31354977545074731373512
Offset: 0
A302557(n) / (exp(-1) * n!) ~ 1 + 2/n^2 + 6/n^3 + 35/n^4 + 256/n^5 + 2187/n^6 + ...
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