A104878 -id:A104878 - cp's OEIS frontend

A053698 a(n) = n^3 + n^2 + n + 1.

1, 4, 15, 40, 85, 156, 259, 400, 585, 820, 1111, 1464, 1885, 2380, 2955, 3616, 4369, 5220, 6175, 7240, 8421, 9724, 11155, 12720, 14425, 16276, 18279, 20440, 22765, 25260, 27931, 30784, 33825, 37060, 40495, 44136, 47989, 52060, 56355, 60880

Offset: 0

Henry Bottomley, Mar 23 2000

a(n) = 1111 in base n.

n^3 + n^2 + n + 1 = (n^2 + 1)*(n + 1), therefore a(n) is never prime. - Alonso del Arte, Apr 22 2014

			a(2) = 15 because 2^3 + 2^2 + 2 + 1 = 8 + 4 + 2 + 1 = 15.
a(3) = 40 because 3^3 + 3^2 + 3 + 1 = 27 + 9 + 3 + 1 = 40.
a(4) = 85 because 4^3 + 4^2 + 4 + 1 = 64 + 16 + 4 + 1 = 85.
From _Bruno Berselli_, Jan 02 2017: (Start)
The terms of the sequence are provided by the row sums of the following triangle (see the seventh formula in the previous section):
.   1;
.   3,   1;
.   9,   5,   1;
.  19,  13,   7,   1;
.  33,  25,  17,   9,   1;
.  51,  41,  31,  21,  11,   1;
.  73,  61,  49,  37,  25,  13,  1;
.  99,  85,  71,  57,  43,  29, 15,  1;
. 129, 113,  97,  81,  65,  49, 33, 17,  1;
. 163, 145, 127, 109,  91,  73, 55, 37, 19,  1;
. 201, 181, 161, 141, 121, 101, 81, 61, 41, 21, 1;
...
Columns from the first to the fifth, respectively: A058331, A001844, A056220 (after -1), A059993, A161532. Also, eighth column is A161549.
(End)

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A237627 (subset of semiprimes).
Cf. A056106 (first differences).
Cf. A062158, A027444, A104878, A055129.

[n^3+n^2+n+1: n in [0..50]]; // Vincenzo Librandi, May 01 2011

A053698:=n->n^3 + n^2 + n + 1; seq(A053698(n), n=0..50); # Wesley Ivan Hurt, Apr 22 2014

Table[n^3 + n^2 + n + 1, {n, 0, 39}] (* Alonso del Arte, Apr 22 2014 *)
FromDigits["1111", Range[0, 50]] (* Paolo Xausa, May 11 2024 *)

Vec((1 + 5*x^2) / (1 - x)^4 + O(x^50)) \\ Colin Barker, Jan 02 2017

def a(n): return (n**3+n**2+n+1) # Torlach Rush, May 08 2024

For n >= 2, a(n) = (n^4-1)/(n-1) = A024002(n)/A024000(n) = A002522(n)*(n+1) = A002061(n+1) + A000578(n).
G.f.: (1+5*x^2) / (1-x)^4. - Colin Barker, Jan 06 2012
a(n) = -A062158(-n). - Bruno Berselli, Jan 26 2016
a(n) = Sum_{i=0..n} 2*n*(n-i)+1. - Bruno Berselli, Jan 02 2017
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 3. - Colin Barker, Jan 02 2017
a(n) = A104878(n+3,n) = A055129(4,n) for n > 0. - Mathew Englander, Jan 06 2021
E.g.f.: exp(x)*(x^3+4*x^2+3*x+1). - Nikolaos Pantelidis, Feb 06 2023

A053699 a(n) = n^4 + n^3 + n^2 + n + 1.

Original entry on oeis.org

1, 5, 31, 121, 341, 781, 1555, 2801, 4681, 7381, 11111, 16105, 22621, 30941, 41371, 54241, 69905, 88741, 111151, 137561, 168421, 204205, 245411, 292561, 346201, 406901, 475255, 551881, 637421, 732541, 837931, 954305, 1082401, 1222981, 1376831, 1544761, 1727605

Offset: 0

Henry Bottomley, Mar 23 2000

a(n) = 11111 in base n.

a(n) = Phi_5(n), where Phi_k is the k-th cyclotomic polynomial.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Carlos M. da Fonseca and Anthony G. Shannon, A formal operator involving Fermatian numbers, Notes Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 491-498.
Michael Penn, What base makes me a perfect square??, YouTube video, 2022.
Index to values of cyclotomic polynomials of integer argument.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

5th row of the array A055129.

Cf. A104878.

[n^4+n^3+n^2+n+1: n in [0..50]]; // Vincenzo Librandi, May 01 2011

A053699 := proc(n)
        numtheory[cyclotomic](5,n) ;
end proc:
seq(A053699(n),n=0..20) ; # R. J. Mathar, Feb 07 2014

f[n_]:=((1+n+n^2+n^3+n^4));Table[f[n],{n,0,6!}] (* Vladimir Joseph Stephan Orlovsky, Mar 03 2010 *)
Join[{1},Table[Total[n^Range[0,4]],{n,40}]] (* Harvey P. Dale, Feb 02 2014 *)

A053699(n):=n^4 + n^3 + n^2 + n + 1$
makelist(A053699(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

a(n)=polcyclo(5,n) \\ Charles R Greathouse IV, Jul 19 2011

a(n) = n^4 + n^3 + n^2 + n + 1 = (n^5-1)/(n-1).
G.f.: (1 + 16*x^2 + 6*x^3 + x^4)/(1-x)^5. - Colin Barker, Jan 10 2012
E.g.f.: exp(x)*(1 + 4*x + 11*x^2 + 7*x^3 + x^4). - Stefano Spezia, Oct 03 2024
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Wesley Ivan Hurt, Aug 05 2025

A069777 Array of q-factorial numbers n!_q, read by ascending antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 6, 3, 1, 1, 1, 24, 21, 4, 1, 1, 1, 120, 315, 52, 5, 1, 1, 1, 720, 9765, 2080, 105, 6, 1, 1, 1, 5040, 615195, 251680, 8925, 186, 7, 1, 1, 1, 40320, 78129765, 91611520, 3043425, 29016, 301, 8, 1, 1

Offset: 0

Franklin T. Adams-Watters, Apr 07 2002

			Square array begins:
    1,   1,    1,      1,       1,        1,         1, ...
    1,   1,    1,      1,       1,        1,         1, ...
    1,   2,    3,      4,       5,        6,         7, ...
    1,   6,   21,     52,     105,      186,       301, ...
    1,  24,  315,   2080,    8925,    29016,     77959, ...
    1, 120, 9765, 251680, 3043425, 22661496, 121226245, ...
    ...

Alois P. Heinz, Antidiagonals n = 0..55, flattened
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
Index entries for sequences related to factorial numbers

Columns q=0..11 are A000012, A000142, A005329, A015001, A015002, A015004, A015005, A015006, A015007, A015008, A015009, A015011.
Rows n=3..5 are A069778, A069779, A218503.
Main diagonal gives A347611.
Cf. A008302, A156173.

A069777 := proc(n,k) local n1: mul(A104878(n1,k), n1=k..n-1) end: A104878 := proc(n,k): if k = 0 then 1 elif k=1 then n elif k>=2 then (k^(n-k+1)-1)/(k-1) fi: end: seq(seq(A069777(n,k), k=0..n), n=0..9); # Johannes W. Meijer, Aug 21 2011
nmax:=9: T(0,0):=1: for n from 1 to nmax do T(n,0):=1:  T(n,1):= (n-1)! od: for q from 2 to nmax do for n from 0 to nmax do T(n+q,q) := product((q^k - 1)/(q - 1), k= 1..n) od: od: for n from 0 to nmax do seq(T(n,k), k=0..n) od; seq(seq(T(n,k), k=0..n), n=0..nmax); # Johannes W. Meijer, Aug 21 2011
# alternative Maple program:
T:= proc(n, k) option remember; `if`(n<2, 1,
      T(n-1, k)*`if`(k=1, n, (k^n-1)/(k-1)))
    end:
seq(seq(T(d-k, k), k=0..d), d=0..10);  # Alois P. Heinz, Sep 08 2021

(* Returns the rectangular array *) Table[Table[QFactorial[n, q], {q, 0, 6}], {n, 0, 6}] (* Geoffrey Critzer, May 21 2017 *)

T(n,q)=prod(k=1, n, ((q^k - 1) / (q - 1))) \\ Andrew Howroyd, Feb 19 2018

T(n,q) = Product_{k=1..n} (q^k - 1) / (q - 1).
T(n,k) = Product_{n1=k..n-1} A104878(n1,k). - Johannes W. Meijer, Aug 21 2011
T(n,k) = Sum_{i>=0} A008302(n,i)*k^i. - Geoffrey Critzer, Feb 26 2025

Name edited by Michel Marcus, Sep 08 2021

A053716 a(n) = 1111111 in base n.

Original entry on oeis.org

7, 127, 1093, 5461, 19531, 55987, 137257, 299593, 597871, 1111111, 1948717, 3257437, 5229043, 8108731, 12204241, 17895697, 25646167, 36012943, 49659541, 67368421, 90054427, 118778947, 154764793, 199411801, 254313151, 321272407, 402321277, 499738093

Offset: 1

Henry Bottomley, Mar 23 2000

Evaluation of the seventh cyclotomic polynomial at n. - Joerg Arndt, Aug 27 2015

			a(3)=1093 because 1111111 base 3=729+243+81+27+9+3+1=121.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Carlos M. da Fonseca and Anthony G. Shannon, A formal operator involving Fermatian numbers, Notes Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 491-498.
Index to values of cyclotomic polynomials of integer argument
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

7th row of the array A055129.

Cf. A104878.

[7] cat [(n^7-1)/(n-1): n in [2..35]]; // Vincenzo Librandi, Feb 08 2014

A053716 := proc(n)
    numtheory[cyclotomic](7,n) ;
end proc:
seq(A053716(n),n=1..20) ; # R. J. Mathar, Feb 07 2014

Table[FromDigits["1111111",n],{n,1,30}](*or*)Table[n^6+n^5+n^4+n^3+n^2+n+1,{n,1,60}] (* Vladimir Joseph Stephan Orlovsky, Jan 29 2012 *)
CoefficientList[Series[-(x^6 - 6 x^5 + 57 x^4 + 232 x^3 + 351 x^2 + 78 x + 7)/(x - 1)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Feb 08 2014 *)

a(n) = n^6+n^5+n^4+n^3+n^2+n+1 = (n^7-1)/(n-1).
G.f.: -x*(x^6-6*x^5+57*x^4+232*x^3+351*x^2+78*x+7)/(x-1)^7. - Colin Barker, Oct 29 2012
E.g.f.: exp(x)*(1 + 6*x + 57*x^2 + 122*x^3 + 76*x^4+ 16*x^5 + x^6) - 1. - Stefano Spezia, Oct 03 2024

A031973 a(n) = Sum_{k=0..n} n^k.

Original entry on oeis.org

1, 2, 7, 40, 341, 3906, 55987, 960800, 19173961, 435848050, 11111111111, 313842837672, 9726655034461, 328114698808274, 11966776581370171, 469172025408063616, 19676527011956855057, 878942778254232811938, 41660902667961039785743, 2088331858752553232964200

Offset: 0

N. J. A. Sloane

These are the generalized repunits of length n+1 in base n for all n >= 1: a(n) expressed in base n is 111...111 (n+1 1's): a(1) = 1^0 + 1^1 = 2 = A000042(2), a(2) = 2^0 + 2^1 + 2^2 = 7 = A000225(3), a(3) = 3^0 + 3^1 + 3^2 + 3^3 = 40 = A003462(4), etc., a(10) = 10^0 + 10^1 + 10^2 + ... + 10^9 + 10^10 = 11111111111 = A002275(11), etc. - Rick L. Shepherd, Aug 26 2004
a(n)=the total number of ordered selections of up to n objects from n types with repetitions allowed.  Thus for 2 objects a,b there are 7 possible selections: aa,bb,ab,ba,a,b, and the null set. - J. M. Bergot, Mar 26 2014
a(n)=the total number of ordered arrangements of 0,1,2..n objects, with repetitions allowed, selected from n types of objects. - J. M. Bergot, Apr 11 2014

			a(3) = 3^0 + 3^1 + 3^2 + 3^3 = 40.

Nathaniel Johnston, Table of n, a(n) for n = 0..100

Cf. A000042 (unary representations), A000225 (2^n-1: binary repunits shown in decimal), A003462 ((3^n-1)/2: ternary repunits shown in decimal), A002275 ((10^n-1)/9: decimal repunits).

Cf. A104878.

[&+[n^k: k in [0..n]]: n in [0..30]]; // Vincenzo Librandi, Apr 18 2011

a:= proc(n) local c, i; c:=1; for i to n do c:= c*n+1 od; c end:
seq(a(n), n=0..20); # Alois P. Heinz, Aug 15 2013

Join[{1},Table[Total[n^Range[0,n]],{n,20}]] (* Harvey P. Dale, Nov 13 2011 *)

a(n)=(n^(n+1)-1)/(n-1) \\ Charles R Greathouse IV, Mar 26 2014

[lucas_number1(n,n,n-1) for n in range(1, 19)] # Zerinvary Lajos, May 16 2009

a(n) = (n^(n+1)-1)/(n-1) = (A007778(n)-1)/(n-1) = A023037(n)+A000312(n) = A031972(n)+1. - Henry Bottomley, Apr 04 2003
a(n) = A125118(n,n-2) for n>2. - Reinhard Zumkeller, Nov 21 2006
a(n) = [x^n] 1/((1 - x)*(1 - n*x)). - Ilya Gutkovskiy, Oct 04 2017
a(n) = A104878(2n,n). - Alois P. Heinz, May 04 2021

A125118 Triangle read by rows: T(n,k) = value of the n-th repunit in base (k+1) representation, 1<=k<=n.

Original entry on oeis.org

1, 3, 4, 7, 13, 21, 15, 40, 85, 156, 31, 121, 341, 781, 1555, 63, 364, 1365, 3906, 9331, 19608, 127, 1093, 5461, 19531, 55987, 137257, 299593, 255, 3280, 21845, 97656, 335923, 960800, 2396745, 5380840, 511, 9841, 87381, 488281, 2015539, 6725601, 19173961, 48427561, 111111111

Offset: 1

Reinhard Zumkeller, Nov 21 2006

			First 4 rows:
1: [1]_2
2: [11]_2 ........ [11]_3
3: [111]_2 ....... [111]_3 ....... [111]_4
4: [1111]_2 ...... [1111]_3 ...... [1111]_4 ...... [1111]_5
_
1: 1
2: 2+1 ........... 3+1
3: (2+1)*2+1 ..... (3+1)*3+1 ..... (4+1)*4+1
4: ((2+1)*2+1)*2+1 ((3+1)*3+1)*3+1 ((4+1)*4+1)*4+1 ((5+1)*5+1)*5+1.

G. C. Greubel, Rows n = 1..50 of the triangle, flattened
Eric Weisstein's World of Mathematics, Repunit

This triangle shares some features with triangle A104878.
This triangle is a portion of rectangle A055129.
Each term of A110737 comes from the corresponding row of this triangle.
Diagonals (adjusting offset as necessary): A060072, A023037, A031973, A173468.
Columns (adjusting offset as necessary): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724, A218725, A218726, A218727, A218728, A218729, A218730, A218731, A218732, A218733, A218734, A132469, A218736, A218737, A218738, A218739, A218740, A218741, A218742, A218743, A218744, A218745, A218746, A218747, A218748, A218749, A218750, A218751, A218753, A218752.
Cf. A023037, A031973, A125119, A125120 (row sums).

[((k+1)^n -1)/k : k in [1..n], n in [1..12]]; // G. C. Greubel, Aug 15 2022

Table[((k+1)^n -1)/k, {n, 12}, {k, n}]//Flatten (* G. C. Greubel, Aug 15 2022 *)

def A125118(n,k): return ((k+1)^n -1)/k
flatten([[A125118(n,k) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Aug 15 2022

T(n, k) = Sum_{i=0..n-1} (k+1)^i.
T(n+1, k) = (k+1)*T(n, k) + 1.
Sum_{k=1..n} T(n, k) = A125120(n).
T(2*n-1, n) = A125119(n).
T(n, 1) = A000225(n).
T(n, 2) = A003462(n) for n>1.
T(n, 3) = A002450(n) for n>2.
T(n, 4) = A003463(n) for n>3.
T(n, 5) = A003464(n) for n>4.
T(n, 9) = A002275(n) for n>8.
T(n, n) = A060072(n+1).
T(n, n-1) = A023037(n) for n>1.
T(n, n-2) = A031973(n) for n>2.
T(n, k) = A055129(n, k+1) = A104878(n+k, k+1), 1<=k<=n. - Mathew Englander, Dec 19 2020

A053700 a(n) = 111111 in base n.

Original entry on oeis.org

6, 63, 364, 1365, 3906, 9331, 19608, 37449, 66430, 111111, 177156, 271453, 402234, 579195, 813616, 1118481, 1508598, 2000719, 2613660, 3368421, 4288306, 5399043, 6728904, 8308825, 10172526, 12356631, 14900788, 17847789, 21243690, 25137931

Offset: 1

Henry Bottomley, Mar 23 2000

			a(3)=364 because 111111 base 3 = 243 + 81 + 27 + 9 + 3 + 1 = 121.

Carlos M. da Fonseca and Anthony G. Shannon, A formal operator involving Fermatian numbers, Notes Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 491-498.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

6th row of the array A055129.

Cf. A104878.

Table[(n^5+n^4+n^3+n^2+n+1),{n,0,5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2010 *)

a(n)=(n^6-1)/(n-1) \\ Charles R Greathouse IV, Sep 28 2015

a(n) = n^5 + n^4 + n^3 + n^2 + n + 1 = (n^6-1)/(n-1).
G.f.: x*(6 + 27*x + 76*x^2 + 6*x^3 + 6*x^4 - x^5)/(1-x)^6. - Colin Barker, May 08 2012
E.g.f.: exp(x)*(1 + 5*x + 26*x^2 + 32*x^3 + 11*x^4+ x^5) - 1. - Stefano Spezia, Oct 03 2024

A053717 a(n) = n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.

Original entry on oeis.org

1, 8, 255, 3280, 21845, 97656, 335923, 960800, 2396745, 5380840, 11111111, 21435888, 39089245, 67977560, 113522235, 183063616, 286331153, 435984840, 648232975, 943531280, 1347368421, 1891142968, 2613136835, 3559590240, 4785883225, 6357828776, 8353082583

Offset: 0

Henry Bottomley, Mar 23 2000

a(n) = 11111111 in base n for n>0.

			a(3) = 3280 because 11111111 base 3 = 2187+729+243+81+27+9+3+1 = 3280.

Carlos M. da Fonseca and Anthony G. Shannon, A formal operator involving Fermatian numbers, Notes Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 491-498.
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

8th row of the array A055129.

Cf. A104878.

Table[FromDigits["11111111",n],{n,1,30}] (* or *) Table[n^7+n^6+n^5+n^4+n^3+n^2+n+1,{n,1,60}] (* Vladimir Joseph Stephan Orlovsky, Jan 29 2012 *)

a(n) = (n^8-1)/(n-1) for n != 1.
G.f.: 1 -x*(x^7-8*x^6-57*x^5-1016*x^4-2297*x^3-1464*x^2-191*x-8)/(x-1)^8. - Colin Barker, Oct 29 2012
E.g.f.: exp(x)*(1 + 7*x + 120*x^2 + 423*x^3 + 426*x^4 + 156*x^5 + 22*x^6 + x^7). - Stefano Spezia, Oct 03 2024
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - Wesley Ivan Hurt, Jun 19 2025

a(0)=1 prepended by Alois P. Heinz, May 04 2021

A104879 Row sums of a sum-of-powers triangle.

Original entry on oeis.org

1, 2, 4, 8, 17, 40, 106, 316, 1049, 3830, 15208, 65072, 297841, 1449756, 7468542, 40555748, 231335961, 1381989882, 8623700812, 56078446616, 379233142801, 2662013133296, 19362917622002, 145719550012300, 1133023004941273, 9090156910550110, 75161929739797520

Offset: 0

Paul Barry, Mar 28 2005

Row sums of A104878.

Cf. A103439 (terms differ by 1), A026898 (first differences).

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

a(n) = 1 + A103439(n). - Mathew Englander, Dec 19 2020

A104881 Triangle T(n,k) = Sum_{j=0..k} (n-k)^(k-j), read by rows.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 7, 4, 1, 1, 5, 13, 15, 5, 1, 1, 6, 21, 40, 31, 6, 1, 1, 7, 31, 85, 121, 63, 7, 1, 1, 8, 43, 156, 341, 364, 127, 8, 1, 1, 9, 57, 259, 781, 1365, 1093, 255, 9, 1, 1, 10, 73, 400, 1555, 3906, 5461, 3280, 511, 10, 1, 1, 11, 91, 585, 2801, 9331, 19531, 21845, 9841, 1023, 11, 1

Offset: 0

Paul Barry, Mar 28 2005

Reverse of triangle A104878.

			Triangle begins as:
  1;
  1, 1;
  1, 2,  1;
  1, 3,  3,  1;
  1, 4,  7,  4, 1;
  1, 5, 13, 15, 5, 1;

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Cf. A104878, A104879 (row sums), A104882 (diagonal sums).

[(&+[ (n-k)^(k-j): j in [0..k]]): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 15 2021

T[n_, k_]:= If[k==n, 1, Sum[(n-k)^(k-j), {j,0,k}]];
Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Jun 15 2021 *)

flatten([[sum((n-k)^(k-j) for j in (0..k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 15 2021

T(n, k) = Sum_{j=0..k} (n-k)^(k-j).
Sum_{k=0..n} T(n, k) = A104879(n).
Sum_{k=0..floor(n/2)} T(k, n-k) = A104882(n).

cp's OEIS Frontend

A053698 a(n) = n^3 + n^2 + n + 1.

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A053699 a(n) = n^4 + n^3 + n^2 + n + 1.

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PARI

Formula

A069777 Array of q-factorial numbers n!_q, read by ascending antidiagonals.

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Maple

Mathematica

PARI

Formula

Extensions

A053716 a(n) = 1111111 in base n.

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Magma

Maple

Mathematica

Formula

A031973 a(n) = Sum_{k=0..n} n^k.

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Magma

Maple

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PARI

Sage

Formula

A125118 Triangle read by rows: T(n,k) = value of the n-th repunit in base (k+1) representation, 1<=k<=n.

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Magma