A045531 -id:A045531 - cp's OEIS frontend

A246049 Number T(n,k) of endofunctions on [n] where the smallest cycle length equals k; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

1, 0, 1, 0, 3, 1, 0, 19, 6, 2, 0, 175, 51, 24, 6, 0, 2101, 580, 300, 120, 24, 0, 31031, 8265, 4360, 2160, 720, 120, 0, 543607, 141246, 74130, 41160, 17640, 5040, 720, 0, 11012415, 2810437, 1456224, 861420, 430080, 161280, 40320, 5040

Offset: 0

Alois P. Heinz, Aug 11 2014

T(0,0) = 1 by convention.

In general, number of endofunctions on [n] where the smallest cycle length equals k is asymptotic to (exp(-H(k-1)) - exp(-H(k))) * n^n, where H(k) is the harmonic number A001008/A002805, k>=1. - Vaclav Kotesovec, Aug 21 2014

			Triangle T(n,k) begins:
  1;
  0,      1;
  0,      3,      1;
  0,     19,      6,     2;
  0,    175,     51,    24,     6;
  0,   2101,    580,   300,   120,    24;
  0,  31031,   8265,  4360,  2160,   720,  120;
  0, 543607, 141246, 74130, 41160, 17640, 5040, 720;
  ...

Alois P. Heinz, Rows n = 0..140, flattened

Columns k=0-10 give: A000007, A045531, A246189, A246190, A246191, A246192, A246193, A246194, A246195, A246196, A246197.
T(2n,n) gives A246050.
Row sums give A000312.
Main diagonal gives A000142(n-1) for n>0.
Cf. A241981, A243098.

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
      add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
      b(n-i*j, i+1), j=0..n/i)))
    end:
A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
T:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), A(n, k) -A(n, k+1)):
seq(seq(T(n, k), k=0..n), n=0..12);

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i>n, 0,
      Sum[(i-1)!^j*multinomial[n, {n-i*j, Sequence @@ Table[i, {j}]}]/j!*
      b[n-i*j, i+1], {j, 0, n/i}]]];
A[n_, k_] := Sum[Binomial[n-1, j-1]*n^(n-j)*b[j, k], {j, 0, n}];
T[n_, k_] := If[k == 0, If[n == 0, 1, 0], A[n, k] - A[n, k+1]];
Table[Table[T[n, k], {k, 0, n}], {n, 0, 12}] // Flatten (* Jean-François Alcover, Jan 06 2015, after Alois P. Heinz *)

A055858 Coefficient triangle for certain polynomials.

Original entry on oeis.org

1, 1, 2, 4, 9, 6, 27, 64, 48, 36, 256, 625, 500, 400, 320, 3125, 7776, 6480, 5400, 4500, 3750, 46656, 117649, 100842, 86436, 74088, 63504, 54432, 823543, 2097152, 1835008, 1605632, 1404928, 1229312, 1075648, 941192, 16777216, 43046721

Offset: 0

Wolfdieter Lang, Jun 20 2000

The coefficients of the partner polynomials are found in triangle A055864.

			{1}; {1,2}; {4,9,6}; {27,64,48,36}; ...
Fourth row polynomial (n=3): p(3,x) = 27 + 64*x + 48*x^2 + 36*x^3.

Column sequences are A000312(n), n >= 1, A055860 (A000169), A055861 (A053506), A055862-3 for m=0..4, row sums: A045531(n+1)= |A039621(n+1, 2)|, n >= 0.

a[n_, m_] /; n < m = 0; a[0, 0] = 1; a[n_, 0] := n^n; a[n_, m_] := n^(m-1)*(n+1)^(n-m+1); Table[a[n, m], {n, 0, 8}, {m, 0, n}] // Flatten (* Jean-François Alcover, Jun 20 2013 *)

a(n, m)=0 if n < m; a(0, 0)=1, a(n, 0) = n^n, n >= 1, a(n, m) = n^(m-1)*(n+1)^(n-m+1), n >= m >= 1;

E.g.f. for column m: A(m, x); A(0, x) = 1/(1+W(-x)); A(1, x) = -1 - (d/dx)W(-x) = -1-W(-x)/((1+W(-x))*x); A(2, x) = A(1, x)-int(A(1, x), x)/x-(1/x+x); recursion: A(m, x) = A(m-1, x)-int(A(m-1, x), x)/x-((m-1)^(m-1))*(x^(m-1))/(m-1)!, m >= 3; W(x) principal branch of Lambert's function.

A055869 a(n) = (n+1)^n - n^n.

Original entry on oeis.org

1, 5, 37, 369, 4651, 70993, 1273609, 26269505, 612579511, 15937424601, 457696700077, 14381984674225, 490839666661891, 18080919199832609, 715027614225987601, 30214447801957316865, 1358671297852359767791, 64780942222614703957417, 3264460344339686410876021

Offset: 1

Wolfdieter Lang, Jun 20 2000

Number of functions f:[n]->[n+1] such that some x in [n] maps to n+1.

Number of switching generators for a power polyadic n-context ({1..k}, ..., {1..k}, <>) with n=k [Theorems 5 and 6, page 81, in Ignatov]. - Dmitry I. Ignatov, Nov 23 2022

G. C. Greubel, Table of n, a(n) for n = 1..385
D. I. Ignatov, On closure operators related to maximal tricliques in tripartite hypergraphs, Discrete Appl. Math., 249 (2018), 74-84.
D. I. Ignatov, Supporting iPython code for enumeration of switching generators of power polyadic n-contexts for n=k<6, GitHub repository.

Row sums of triangle A055864.

Cf. A055864, A055858, A045531.

[(n+1)^n - n^n: n in [1..40]]; // Vincenzo Librandi, Jan 11 2015

Table[(n+1)^n-n^n,{n,40}] (* Vladimir Joseph Stephan Orlovsky, Nov 20 2009 *)

vector(20, n, (n+1)^n - n^n) \\ Michel Marcus, Jan 10 2015

E.g.f.: W(-x)*(x-1)/((1+W(-x))*x), W(x) principal branch of Lambert's function.
a(n) = Sum_{m=1..n} A055864(n, m).
a(n) = Sum_{i=0..n-1} n^i*C(n, i). - Olivier Gérard, Jun 26 2001
With interpolated zeros, ceiling(n/2)^floor(n/2) - floor(n/2)^floor(n/2). - Paul Barry, Jul 13 2005
a(n) = Sum_{k=1..n} (-1)^(n-k)*k!*Stirling2(n,k)*binomial(n+k-1,n). - Vladimir Kruchinin, Sep 20 2015

More terms from Vincenzo Librandi, Jan 11 2015

A354794 Triangle read by rows. The Bell transform of the sequence {m^m | m >= 0}.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 4, 3, 1, 0, 27, 19, 6, 1, 0, 256, 175, 55, 10, 1, 0, 3125, 2101, 660, 125, 15, 1, 0, 46656, 31031, 9751, 1890, 245, 21, 1, 0, 823543, 543607, 170898, 33621, 4550, 434, 28, 1, 0, 16777216, 11012415, 3463615, 688506, 95781, 9702, 714, 36, 1

Offset: 0

Peter Luschny, Jun 09 2022

For the definition of the Bell transform see A264428. The Bell transform of {(-m)^m | m >= 0} is A039621. The numbers A039621(n, k) are known as the Lehmer-Comtet numbers of 2nd kind. We think it is more natural to use Bell_{n, k}({m^m}) as the basis for the definition (and let the triangle start at (0, 0)).

			Triangle T(n, k) begins:
[0] 1;
[1] 0,        1;
[2] 0,        1,        1;
[3] 0,        4,        3,       1;
[4] 0,       27,       19,       6,      1;
[5] 0,      256,      175,      55,     10,     1;
[6] 0,     3125,     2101,     660,    125,    15,    1;
[7] 0,    46656,    31031,    9751,   1890,   245,   21,   1;
[8] 0,   823543,   543607,  170898,  33621,  4550,  434,  28,  1;
[9] 0, 16777216, 11012415, 3463615, 688506, 95781, 9702, 714, 36, 1;

Louis Comtet, Advanced Combinatorics. Reidel, Dordrecht, 1974, p. 139-140.

D. H. Lehmer, Numbers Associated with Stirling Numbers and x^x, Rocky Mountain J. Math., 15(2) 1985, pp. 461-475.
Peter Luschny, The Bell transform
Wikipedia, Bell polynomials.

Cf. A264428, A039621 (signed variant), A195979 (row sums), A000312 (column 1), A045531 (column 2), A281596 (column 3), A281595 (column 4), A000217 (diagonal 1), A215862 (diagonal 2), A354795 (matrix inverse), A137452 (Abel).

T := (n, k) -> if n = k then 1 else
add((-1)^j*(n-j-1)^(n-1)/(j!*(k-1-j)!), j = 0.. k-1) fi:
seq(seq(T(n, k), k = 0..n), n = 0..9);
# Alternatively, using the function BellMatrix from A264428:
BellMatrix(n -> n^n, 9);
# Or by recursion:
R := proc(n, k, m) option remember;
   if k < 0 or n < 0 then 0 elif k = 0 then 1 else
   m*R(n, k-1, m) + R(n-1, k, m+1) fi end:
A039621 := (n, k) -> ifelse(n = 0, 1, R(k-1, n-k, n-k)):

Unprotect[Power]; Power[0, 0] = 1; pow[n_] := n^n;
R = Range[0, 9]; T[n_, k_] := BellY[n, k, pow[R]];
Table[T[n, k], {n, R}, {k, 0, n}] // Flatten

from functools import cache
@cache
def t(n, k, m):
    if k < 0 or n < 0: return 0
    if k == 0: return n ** k
    return m * t(n, k - 1, m) + t(n - 1, k, m + 1)
def A354794(n, k): return t(k - 1, n - k, n - k) if n != k else 1
for n in range(9): print([A354794(n, k) for k in range(n + 1)])

T(n, k) = Bell_{n, k}(A000312), where Bell_{n, k} is the partial Bell polynomial evaluated over the powers m^m (with 0^0 = 1). See the Mathematica program.
T(n, k) = Sum_{j=0..k-1} (-1)^j*(n-j-1)^(n - 1)/(j! * (k-1-j)!) for 0 <= k < n and T(n, n) = 1.
T(n, k) = r(k-1, n-k, n-k) for n,k >= 1 and T(0, 0) = 1, where r(n, k, m) = m*r(n, k-1, m) + r(n-1, k, m+1) and r(n, 0, m) = 1. (see Vladimir Kruchinin's formula in A039621).
Sum_{k=1..n} binomial(k + x - 1, k-1)*(k-1)!*T(n, k) = (n + x)^(n - 1) for n >= 1.
Sum_{k=1..n} (-1)^(k+j)*Stirling1(k, j)*T(n, k) = n^(n-j)*binomial(n-1, j-1) for n >= 1, which are, up to sign, the coefficients of the Abel polynomials (A137452).
From Werner Schulte, Jun 14 2022 and Jun 19 2022: (Start)
E.g.f. of column k >= 0: (Sum_{i>0} (i-1)^(i-1) * t^i / i!)^k / k!.
Conjecture: T(n, k) = Sum_{i=0..n-k} A048994(n-k, i) * A048993(n+i-1, n-1) for 0 < k <= n and T(n, 0) = 0^n for n >= 0; proved by Mike Earnest, see link at A354797. (End)

A066274 Number of endofunctions of [n] such that 1 is not a fixed point.

Original entry on oeis.org

0, 2, 18, 192, 2500, 38880, 705894, 14680064, 344373768, 9000000000, 259374246010, 8173092077568, 279577021469772, 10318292052303872, 408700964355468750, 17293822569102704640, 778579070010669895696, 37160496515557841043456, 1874292305362402347591138

Offset: 1

Len Smiley, Dec 09 2001

nonn

a(n) is the number of functional digraphs that are not a solitary rooted tree. - Geoffrey Critzer, Aug 31 2013
For n > 1 a(n) is the number of numbers with n digits in base n. - Gionata Neri, Feb 18 2016
a(n) is the number of pairs of adjacent equal letters in all n-ary words of length n. - John Tyler Rascoe, Nov 19 2024

			a(2)=2: [1->2,2->1], [1->2,2->2].

Vincenzo Librandi, Table of n, a(n) for n = 1..300
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Cf. A045531, A066275.

[n^n - n^(n-1): n in [1..20]]; // Vincenzo Librandi, Aug 02 2011

Table[(n-1)*n^(n-1), {n, 1, 20}] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *)

a(n) = n^n - n^(n-1).
E.g.f.: T^2/(1-T), where T=T(x) is Euler's tree function (see A000169).
For n > 1 a(n)=1/(Integral_{x=n..infinity} 1/x^n dx). - Francesco Daddi, Aug 01 2011
a(n) = sum(i=1..n-1, C(n,i)*(i^i*(n-i)^(n-i-1))). - Vladimir Kruchinin May 15 2013
E.g.f.: x^2*A''(x) where A(x) is the e.g.f. for A000272. - Geoffrey Critzer, Aug 31 2013
a(n) = 2*A081131(n) = 2*|A070896(n)|. - Geoffrey Critzer, Aug 31 2013

A199656 Triangular array read by rows, T(n,k) is the number of functions from {1,2,...,n} into {1,2,...,n} with maximum value of k.

Original entry on oeis.org

1, 1, 3, 1, 7, 19, 1, 15, 65, 175, 1, 31, 211, 781, 2101, 1, 63, 665, 3367, 11529, 31031, 1, 127, 2059, 14197, 61741, 201811, 543607, 1, 255, 6305, 58975, 325089, 1288991, 4085185, 11012415, 1, 511, 19171, 242461, 1690981, 8124571, 30275911, 93864121, 253202761

Offset: 1

Geoffrey Critzer, Nov 08 2011

Row sums = A000312.

Main diagonal = A045531.

			Triangle begins:
  1
  1    3
  1    7   19
  1   15   65   175
  1   31  211   781   2101
  1   63  665  3367  11529   31031
  1  127 2059 14197  61741  201811  543607
  ...

Vincenzo Librandi, Rows n = 1..60, flattened

Cf. A022522, A022523.

/* As triangle: */ [[k^n - (k-1)^n: k in [1..n]]: n in [1..9]]; // Vincenzo Librandi, Jan 28 2013

Table[Table[(1-((i-1)/i)^n) i^n,{i,1,n}],{n,1,8}]//Grid
Flatten[Table[k^n - (k-1)^n, {n, 0, 10}, {k, 1, n}]] (* Vincenzo Librandi, Jan 28 2013 *)

T(n,k) = k^n-(k-1)^n.

A039621 Triangle of Lehmer-Comtet numbers of 2nd kind.

Original entry on oeis.org

1, -1, 1, 4, -3, 1, -27, 19, -6, 1, 256, -175, 55, -10, 1, -3125, 2101, -660, 125, -15, 1, 46656, -31031, 9751, -1890, 245, -21, 1, -823543, 543607, -170898, 33621, -4550, 434, -28, 1, 16777216, -11012415, 3463615, -688506, 95781, -9702, 714, -36, 1

Offset: 1

Len Smiley

Also the Bell transform of (-n)^n adding 1,0,0,0,... as column 0. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 16 2016

			The triangle T(n, k) begins:
[1]       1;
[2]      -1,      1;
[3]       4,     -3,       1;
[4]     -27,     19,      -6,     1;
[5]     256,   -175,      55,   -10,     1;
[6]   -3125,   2101,    -660,   125,   -15,   1;
[7]   46656, -31031,    9751, -1890,   245, -21,   1;
[8] -823543, 543607, -170898, 33621, -4550, 434, -28, 1;

D. H. Lehmer, Numbers Associated with Stirling Numbers and x^x, Rocky Mountain J. Math., 15(2) 1985, pp. 461-475.

A008296 (matrix inverse), A354794 (variant), A045531 (column |a(n, 2)|).

Cf. A185164.

R := proc(n, k, m) option remember;
   if k < 0  or n < 0 then 0 elif k = 0 then 1 else
   m*R(n, k-1, m) + R(n-1, k, m+1) fi end:
A039621 := (n, k) -> (-1)^(n-k)*R(k-1, n-k, n-k):
seq(seq(A039621(n, k), k = 1..n), n = 1..9); # Peter Luschny, Jun 10 2022 after Vladimir Kruchinin

a[1, 1] = 1; a[n_, k_] := 1/(k-1)! Sum[((-1)^(n-k-i)*Binomial[k-1, i]*(n-i-1)^(n-1)), {i, 0, k-1}];
Table[a[n, k], {n, 1, 10}, {k, 1, n}]//Flatten (* Jean-François Alcover, Jun 03 2019 *)

T(n,k,m):=if k<0 or n<0 then 0 else if k=0 then 1 else m*T(n,k-1,m)+T(n-1,k,m+1);
a(n,k):=if nVladimir Kruchinin, Mar 07 2020

tabl(nn) = {for (n = 1, nn, for (k = 1, n, print1(sum(i = 0, k-1,(-1)^(n-k-i)*binomial(k-1, i)*(n-i-1)^(n-1))/(k-1)!, ", ");); print(););} \\ Michel Marcus, Aug 28 2013

# uses[bell_matrix from A264428]
# Adds 1,0,0,0,... as column 0 at the left side of the triangle.
bell_matrix(lambda n: (-n)^n, 7) # Peter Luschny, Jan 16 2016

(k-1)!*a(n, k) = Sum_{i=0..k-1}((-1)^(n-k-i)*binomial(k-1, i)*(n-i-1)^(n-1)).

a(n,k) = (-1)^(n-k)*T(k,n-k,n-k), n>=k, where T(n,k,m)=m*T(n,m-1,k)+T(n-1,k,m+1), T(n,0,m)=1. - Vladimir Kruchinin, Mar 07 2020

A281596 a(n) = ((n-2)^n - 2*(n-1)^n + n^n)/2.

Original entry on oeis.org

0, 0, 1, 6, 55, 660, 9751, 170898, 3463615, 79669320, 2050086511, 58346365110, 1819621847407, 61705703989020, 2260586259354151, 88971796139662842, 3743940350046570751, 167735288431662235920, 7971302827015366403551, 400510700317394780627934, 21212944650652080893863087

Offset: 0

Peter Luschny, Jan 26 2017

nonn

Paolo Xausa, Table of n, a(n) for n = 0..380

Cf. A000312, A045531, A281595.

a := n -> ((n-2)^n-2*(n-1)^n+n^n)/2:
seq(a(n), n=0..21);

A281596[n_] := If[n == 0, 0, ((n-2)^n - 2*(n-1)^n + n^n)/2];
Array[A281596, 25, 0] (* Paolo Xausa, Jul 10 2024 *)

a(n) ~ n^n*(1/2+(1/2-1/n)*e^(-2)+(1/(2*n)-1)*e^(-1)).

A060226 a(n) = n^n - n*(n-1)^(n-1).

Original entry on oeis.org

1, 0, 2, 15, 148, 1845, 27906, 496951, 10188872, 236425545, 6125795110, 175311670611, 5492360400924, 186965800764925, 6871755333266474, 271213787997489135, 11440441827615801616, 513645612633274386705

Offset: 0

Henry Bottomley, Jul 12 2001

nonn

For n > 0, a(n) = number of endofunctions of [n] mapping some x<>1 to 1. - Len Smiley, Nov 15 2001 (Endofunction interpretation from a(n) = n*(n^(n-1) - (n-1)^(n-1)).)

Harry J. Smith, Table of n, a(n) for n = 0..100
D. Callan, A Bijection between Marked Trees
Leonard Smiley, Problem 10781, Amer. Math. Monthly, 107, Feb. 2000, p. 176.

Cf. A000312, A045531, A055869.

a060226 0 = 1
a060226 n = a000312 n - n * a000312 (n - 1)
-- Reinhard Zumkeller, Aug 27 2012

A060226:= func< n | n^n - n*(n-1)^(n-1) >;
[A060226(n): n in [0..30]]; // G. C. Greubel, Nov 03 2024

f := n-> n*sum(binomial(n-1,j-1)*(n-1)^(n-j), j=2..n);
g := n-> n^n -n*(n-1)^(n-1);
h := n-> sum(binomial(n,j)*j^(j-1)*(n-j)^(n-j), j=2..n);
k := n-> sum(binomial(n,j-1)*(j-1)^(j-1)*(n-j)^(n-j), j=2..n); # then a(n)=f(n)=g(n)=h(n)=k(n)

Join[{1,0},Table[n^n-n*(n-1)^(n-1),{n,2,20}]] (* Harvey P. Dale, Nov 16 2012 *)

{ for (n=0, 100, write("b060226.txt", n, " ", n^n - n*(n - 1)^(n - 1)); ) } \\ Harry J. Smith, Jul 03 2009

def A060226(n): return n^n - n*(n-1)^(n-1)
[A060226(n) for n in range(31)] # G. C. Greubel, Nov 03 2024

a(n) = n*A055869(n-1).
Limit_{n -> oo} ( a(n)/a(n-1) - a(n-1)/a(n-2) ) -> e.
E.g.f.: (1-x)/(1-T), where T=T(x) is Euler's tree function (see A000169). The e.g.f. for n > 0 terms only (applicable to endofunctions) is (T - x)/(1 - T). - Len Smiley, Dec 10 2001

A350134 Number of endofunctions on [n] with at least one isolated fixed point.

Original entry on oeis.org

0, 1, 1, 10, 87, 1046, 15395, 269060, 5440463, 124902874, 3208994379, 91208536112, 2841279322871, 96258245162678, 3523457725743059, 138573785311560916, 5827414570508386335, 260928229315498155314, 12393729720071855683739, 622422708333615857463608

Offset: 0

Alois P. Heinz, Dec 15 2021

nonn

			a(3) = 10: 123, 122, 133, 132, 121, 323, 321, 113, 223, 213.

Alois P. Heinz, Table of n, a(n) for n = 0..386

Column k=1 of A347999.

Cf. A000312, A001865, A045531, A069856, A204042, A350212.

g:= proc(n) option remember; add(n^(n-j)*(n-1)!/(n-j)!, j=1..n) end:
b:= proc(n, t) option remember; `if`(n=0, t, add(g(i)*
      b(n-i, `if`(i=1, 1, t))*binomial(n-1, i-1), i=1..n))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..23);

g[n_] := g[n] = Sum[n^(n - j)*(n - 1)!/(n - j)!, {j, 1, n}];
b[n_, t_] := b[n, t] = If[n == 0, t, Sum[g[i]*
     b[n - i, If[i == 1, 1, t]]*Binomial[n - 1, i - 1], {i, 1, n}]];
a[n_] := b[n, 0];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Apr 27 2022, after Alois P. Heinz *)

a(n) = A000312(n) - abs(A069856(n)).

a(n) = Sum_{k=1..n} A350212(n,k).

cp's OEIS Frontend

A246049 Number T(n,k) of endofunctions on [n] where the smallest cycle length equals k; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

A055858 Coefficient triangle for certain polynomials.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Formula

A055869 a(n) = (n+1)^n - n^n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

Extensions

A354794 Triangle read by rows. The Bell transform of the sequence {m^m | m >= 0}.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Maple

Mathematica

Python

Formula

A066274 Number of endofunctions of [n] such that 1 is not a fixed point.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A199656 Triangular array read by rows, T(n,k) is the number of functions from {1,2,...,n} into {1,2,...,n} with maximum value of k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A039621 Triangle of Lehmer-Comtet numbers of 2nd kind.

Views

Author

Keywords

Comments

Examples

Links