cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A045756 Expansion of e.g.f. (1-9*x)^(-1/9), 9-factorial numbers.

Original entry on oeis.org

1, 1, 10, 190, 5320, 196840, 9054640, 498005200, 31872332800, 2326680294400, 190787784140800, 17361688356812800, 1736168835681280000, 189242403089259520000, 22330603564532623360000, 2835986652695643166720000, 385694184766607470673920000, 55925656791158083247718400000
Offset: 0

Views

Author

Wolfdieter Lang

Keywords

Comments

Nine-fold factorials of numbers 9k+1, k = 0, 1, 2, ... - M. F. Hasler, Feb 14 2020

Links

Crossrefs

Cf. A008542, A048994, A114806 (9-fold factorials), A132393.
Cf. k-fold factorials : A000142 ("1-fold"), A001147 (2-fold), A007559 (3), A007696 (4), A008548 (5), A008542 (6), A045754 (7), A045755 (8), A144773 (10), A256268 (combined table).

Programs

  • GAP
    List([0..20], n-> Product([0..n-1], j-> 9*j+1) ); # G. C. Greubel, Nov 11 2019
  • Magma
    [1] cat [(&*[9*j+1: j in [0..n-1]]): n in [1..20]]; // G. C. Greubel, Nov 11 2019
  • Maple
    seq( mul(9*j+1, j=0..n-1), n=0..20); # G. C. Greubel, Nov 11 2019
  • Mathematica
    Table[9^n*Pochhammer[1/9, n], {n,0,20}] (* G. C. Greubel, Nov 11 2019 *)
  • PARI
    vector(21, n, prod(j=0,n-2, 9*j+1) ) \\ G. C. Greubel, Nov 11 2019
  • Sage
    [product( (9*j+1) for j in (0..n-1)) for n in (0..20)] # G. C. Greubel, Nov 11 2019

Formula

a(n+1) = (9*n+1)(!^9) = Product_{k=0..n-1} (9*k+1), n >= 0.
E.g.f. (1-9*x)^(-1/9).
D-finite with recurrence: a(n) +(-9*n+8)*a(n-1)=0. - R. J. Mathar, Jan 17 2020
a(n) = A114806(9n-8). - M. F. Hasler, Feb 14 2020
a(n) = Sum_{k = 0..n} (-9)^(n - k) * A048994(n, k) = Sum_{k = 0..n} 9^(n - k) * A132393(n, k). Philippe Deléham, Sep 20 2008
a(n) = (-8)^n * sum_{k = 0..n} (9/8)^k * s(n + 1, n + 1 - k), where s(n, k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012
a(n) = 9^n * Gamma(n + 1/9) / Gamma(1/9). - Artur Jasinski Aug 23 2016
a(n) ~ sqrt(2 * Pi) * 9^n * n^(n - 7/18)/(Gamma(1/9) * exp(n)). - Ilya Gutkovskiy, Sep 10 2016
Sum_{n>=0} 1/a(n) = 1 + (e/9^8)^(1/9)*(Gamma(1/9) - Gamma(1/9, 1/9)). - Amiram Eldar, Dec 21 2022

Extensions

a(0)=1 inserted; merged with A144772; formulas and programs changed accordingly by Georg Fischer, Feb 15 2020

A092985 a(n) is the product of the first n terms of an arithmetic progression with the first term 1 and common difference n.

Original entry on oeis.org

1, 1, 3, 28, 585, 22176, 1339975, 118514880, 14454403425, 2326680294400, 478015854767451, 122087424094272000, 37947924636264267625, 14105590169042424729600, 6178966019176767549393375, 3150334059785191453342744576, 1849556085478041490537172810625
Offset: 0

Views

Author

Amarnath Murthy, Mar 28 2004

Keywords

Comments

We have the triangle (chopped versions of A076110, A162609)
1;
1 3;
1 4 7;
1 5 9 13;
1 6 11 16 21;
1 7 13 19 25 31;
...
Sequence contains the product of the terms of the rows.
a(n) = b(n-1) where b(n) = n^n*Gamma(n+1/n)/Gamma(1/n) and b(0) is limit n->0+ of b(n). - Gerald McGarvey, Nov 10 2007
Product of the entries in the first column of an n X n square array with elements 1..n^2 listed in increasing order by rows. - Wesley Ivan Hurt, Apr 02 2025

Examples

			a(5) = 1*6*11*16*21 = 22176.

Links

Crossrefs

Cf. A057237, A092987.
Main diagonal of A256268.

Programs

  • GAP
    List([0..20], n-> Product([0..n-1], j-> j*n+1) ); # G. C. Greubel, Mar 04 2020
  • Magma
    [1] cat [ (&*[j*n+1: j in [0..n-1]]): n in [1..20]]; // G. C. Greubel, Mar 04 2020
  • Maple
    a:= n-> mul(n*j+1, j=0..n-1):
seq(a(n), n=0..20);  # Alois P. Heinz, Nov 24 2015
  • Mathematica
    Flatten[{1, Table[n^n * Pochhammer[1/n, n], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 05 2018 *)
  • PARI
    vector(21, n, my(m=n-1); prod(j=0,m-1, j*m+1)) \\ G. C. Greubel, Mar 04 2020
  • Sage
    [product(j*n+1 for j in (0..n-1)) for n in (0..20)] # G. C. Greubel, Mar 04 2020

Formula

a(n) = Product_{k=1..n} (1+(k-1)*n) = 1*(1+n)*(1+2n)*...*(n^2-n+1).
a(n) = Sum_{k=0..n} (-1)^(n-k)*Stirling1(n, k)*n^(n-k). - Vladeta Jovovic, Jan 28 2005
a(n) = n! * [x^n] 1/(1 - n*x)^(1/n) for n > 0. - Ilya Gutkovskiy, Oct 05 2018
a(n) ~ sqrt(2*Pi) * n^(2*n - 3/2) / exp(n). - Vaclav Kotesovec, Oct 05 2018

Extensions

More terms from Erich Friedman, Aug 08 2005
Offset corrected by Alois P. Heinz, Nov 24 2015

A303489 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals: A(n,k) = n! * [x^n] 1/(1 - k*x)^(n/k).

Original entry on oeis.org

1, 1, 1, 1, 1, 6, 1, 1, 8, 60, 1, 1, 10, 105, 840, 1, 1, 12, 162, 1920, 15120, 1, 1, 14, 231, 3640, 45045, 332640, 1, 1, 16, 312, 6144, 104720, 1290240, 8648640, 1, 1, 18, 405, 9576, 208845, 3674160, 43648605, 259459200, 1, 1, 20, 510, 14080, 375000, 8648640, 152152000, 1703116800, 8821612800
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 24 2018

Keywords

Examples

			Square array begins:
      1,      1,       1,       1,       1,       1,  ...
      1,      1,       1,       1,       1,       1,  ...
      6,      8,      10,      12,      14,      16,  ...
     60,    105,     162,     231,     312,     405,  ...
    840,   1920,    3640,    6144,    9576,   14080,  ...
  15120,  45045,  104720,  208845,  375000,  623645,  ...
=========================================================
A(1,1) = 1;
A(2,1) = 2*3 = 6;
A(3,1) = 3*4*5 = 60;
A(4,1) = 4*5*6*7 = 840;
A(5,1) = 5*6*7*8*9 = 15120, etc.
...
A(1,2) = 1;
A(2,2) = 2*4 = 8;
A(3,2) = 3*5*7 = 105;
A(4,2) = 4*6*8*10 = 1920;
A(5,2) = 5*7*9*11*13 = 45045, etc.
...
A(1,3) = 1;
A(2,3) = 2*5 = 10;
A(3,3) = 3*6*9 = 162;
A(4,3) = 4*7*10*13 = 3640;
A(5,3) = 5*8*11*14*17 = 104720, etc.
...

Links

Crossrefs

Columns k=1..5 give A000407, A113551, A303486, A303487, A303488.
Main diagonal gives A061711.
Cf. A008279, A131182, A256268, A265609.

Programs

  • Mathematica
    Table[Function[k, n! SeriesCoefficient[1/(1 - k x)^(n/k), {x, 0, n}]][j - n + 1], {j, 0, 9}, {n, 0, j}] // Flatten
Table[Function[k, Product[k i + n, {i, 0, n - 1}]][j - n + 1], {j, 0, 9}, {n, 0, j}] // Flatten
Table[Function[k, k^n Pochhammer[n/k, n]][j - n + 1], {j, 0, 9}, {n, 0, j}] // Flatten

Formula

A(n,k) = Product_{j=0..n-1} (k*j + n).

A144773 10-fold factorials: Product_{k=0..n-1} (10*k+1).

Original entry on oeis.org

1, 1, 11, 231, 7161, 293601, 14973651, 913392711, 64850882481, 5252921480961, 478015854767451, 48279601331512551, 5359035747797893161, 648443325483545072481, 84946075638344404495011, 11977396665006561033796551, 1808586896415990716103279201, 291182490322974505292627951361
Offset: 0

Views

Author

Philippe Deléham, Sep 21 2008

Keywords

Links

Crossrefs

Essentially a duplicate of A045757.
Cf. k-fold factorials: A000142 ("1-fold"), A001147 (2-fold), A007559 (3), A007696 (4), A008548 (5), A008542 (6), A045754 (7), A045755 (8), A045756 (9), A256268 (combined table).
Cf. A048994, A132393.

Programs

  • Magma
    R:=PowerSeriesRing(Rationals(), 15); Coefficients(R!(Laplace( (1-10*x)^(-1/10) ))); // G. C. Greubel, Mar 03 2020
  • Maple
    G(x):=(1-10*x)^(-1/10): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..14); # Zerinvary Lajos, Apr 03 2009
  • Mathematica
    b = 10; Table[FullSimplify[b^n*Gamma[n + 1/b]/Gamma[1/b]], {n, 0, 14}] (* Michael De Vlieger, Sep 14 2016 *)
Join[{1},FoldList[Times,10 Range[0,15]+1]] (* Harvey P. Dale, Oct 24 2022 *)
  • PARI
    Vec(serlaplace( (1-10*x)^(-1/10) +O('x^15) )) \\ G. C. Greubel, Mar 03 2020
  • Sage
    [10^n*rising_factorial(1/10,n) for n in (0..15)] # G. C. Greubel, Mar 03 2020

Formula

a(n) = Sum_{k = 0..n} (-10)^(n - k) * A048994(n, k).
a(n) = Sum_{k = 0..n} 10^(n - k) * A132393(n, k).
E.g.f.: (1 - 10*x)^(-1/10).
a(n) = A045757(n), n>0.
a(n) = (-9)^n * Sum_{k = 0..n} (10/9)^k * s(n + 1,n + 1 - k), where s(n, k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012
G.f.: 1/Q(0), where Q(k) = 1 - (10*k+1)*x/( 1 - 10*x*(k+1)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Jan 09 2014
a(n) = 10^n * Gamma(n + 1/10) / Gamma(1/10). - Artur Jasinski Aug 23 2016
a(n) ~ sqrt(2*Pi)*10^n*n^(n-2/5)/(Gamma(1/10)*exp(n)). - Ilya Gutkovskiy, Sep 11 2016
D-finite with recurrence: a(n) - (10*n-9)*a(n-1) = 0. - R. J. Mathar, Jan 20 2020
Sum_{n>=0} 1/a(n) = 1 + (e/10^9)^(1/10)*(Gamma(1/10) - Gamma(1/10, 1/10)). - Amiram Eldar, Dec 22 2022

A153274 Triangle, read by rows, T(n,k) = k^(n+1) * Pochhammer(1/k, n+1).

Original entry on oeis.org

2, 6, 15, 24, 105, 280, 120, 945, 3640, 9945, 720, 10395, 58240, 208845, 576576, 5040, 135135, 1106560, 5221125, 17873856, 49579075, 40320, 2027025, 24344320, 151412625, 643458816, 2131900225, 5925744000, 362880, 34459425, 608608000, 4996616625, 26381811456, 104463111025, 337767408000, 939536222625
Offset: 1

Views

Author

Roger L. Bagula, Dec 22 2008

Keywords

Comments

A Pochhammer function-based triangular sequence.
Row sums are: {2, 21, 409, 14650, 854776, 73920791, 8878927331, 1413788600036, 288152651134776, 73152069870215127, ...}.

Examples

			Triangle begins as:
      2;
      6,      15;
     24,     105,      280;
    120,     945,     3640,      9945;
    720,   10395,    58240,    208845,    576576;
   5040,  135135,  1106560,   5221125,  17873856,   49579075;
  40320, 2027025, 24344320, 151412625, 643458816, 2131900225, 5925744000;

Links

Crossrefs

Cf. A000142, A001147, A007559, A007696, A008548, A008542, A045754, A045755, A045756.
Cf. A142589, A256268.

Programs

  • GAP
    Flat(List([1..12], n-> List([1..n], k-> Product([0..n], j-> j*k+1 )))); # G. C. Greubel, Mar 05 2020
  • Magma
    [(&*[j*k+1: j in [0..n]]): k in [1..n], n in [1..12]]; // G. C. Greubel, Mar 05 2020
  • Maple
    seq(seq( k^(n+1)*pochhammer(1/k, n+1), k=1..n), n=1..12); # G. C. Greubel, Mar 05 2020
  • Mathematica
    Table[Apply[Plus, CoefficientList[j*k^n*Pochhammer[(j+k)/k, n], j]], {n, 12}, {k,n}]//Flatten (* modified by G. C. Greubel, Mar 05 2020 *)
Table[k^(n+1)*Pochhammer[1/k, n+1], {n,12}, {k,n}]//Flatten (* G. C. Greubel, Mar 05 2020 *)
  • PARI
    T(n, k) = prod(j=0, n, j*k+1);
for(n=1, 12, for(k=1, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Mar 05 2020
  • Sage
    [[k^(n+1)*rising_factorial(1/k,n+1) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Mar 05 2020

Formula

T(n, k) = k^(n+1) * Pochmammer(1/k, n+1).
T(n, k) = Product_{j=0..n} (j*k + 1). - G. C. Greubel, Mar 05 2020

Extensions

Edited by G. C. Greubel, Mar 05 2020

A349971 Array read by ascending antidiagonals, A(n, k) = -(-n)^k*FallingFactorial(1/n, k) for n, k >= 1.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 10, 15, 0, 1, 4, 21, 80, 105, 0, 1, 5, 36, 231, 880, 945, 0, 1, 6, 55, 504, 3465, 12320, 10395, 0, 1, 7, 78, 935, 9576, 65835, 209440, 135135, 0, 1, 8, 105, 1560, 21505, 229824, 1514205, 4188800, 2027025, 0
Offset: 1

Views

Author

Peter Luschny, Dec 21 2021

Keywords

Examples

			Array starts:
[1] 1, 0,   0,    0,      0,       0,         0,           0, ... A000007
[2] 1, 1,   3,   15,    105,     945,     10395,      135135, ... A001147
[3] 1, 2,  10,   80,    880,   12320,    209440,     4188800, ... A008544
[4] 1, 3,  21,  231,   3465,   65835,   1514205,    40883535, ... A008545
[5] 1, 4,  36,  504,   9576,  229824,   6664896,   226606464, ... A008546
[6] 1, 5,  55,  935,  21505,  623645,  21827575,   894930575, ... A008543
[7] 1, 6,  78, 1560,  42120, 1432080,  58715280,  2818333440, ... A049209
[8] 1, 7, 105, 2415,  74865, 2919735, 137227545,  7547514975, ... A049210
[9] 1, 8, 136, 3536, 123760, 5445440, 288608320, 17893715840, ... A049211
Triangle starts:
[1] [1]
[2] [1, 0]
[3] [1, 1,  0]
[4] [1, 2,  3,   0]
[5] [1, 3, 10,  15,    0]
[6] [1, 4, 21,  80,  105,     0]
[7] [1, 5, 36, 231,  880,   945,      0]
[8] [1, 6, 55, 504, 3465, 12320,  10395,      0]
[9] [1, 7, 78, 935, 9576, 65835, 209440, 135135, 0]

Links

Crossrefs

Rows 1-9: A000007, A001147, A008544, A008545, A008546, A008543, A049209, A049210, A049211.
Main diagonal A349731.
Cf. A158886, A256268.

Programs

  • Magma
    [k eq n select 0^(n-1) else Round((n-k+1)^(k-1)*Gamma(k-1 + (n-k)/(n-k+1))/Gamma((n-k)/(n-k+1))): k in [1..n], n in [1..10]]; // G. C. Greubel, Feb 22 2022
  • Mathematica
    A[n_, k_] := -(-n)^k * FactorialPower[1/n, k]; Table[A[n - k + 1, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Amiram Eldar, Dec 21 2021 *)
  • SageMath
    def A(n, k): return -(-n)^k*falling_factorial(1/n, k)
def T(n, k): return A(n-k+1, k)
for n in (1..9): print([A(n, k) for k in (1..8)])
for n in (1..9): print([T(n, k) for k in (1..n)])

Formula

From G. C. Greubel, Feb 22 2022: (Start)
A(n, k) = n^(k-1)*Pochhammer((n-1)/n, k-1) (array).
T(n, k) = (n-k+1)^(k-1)*Pochhammer((n-k)/(n-k+1), k-1) (antidiagonal triangle).
T(2*n, n) = (-1)^(n-1)*A158886(n). (End)

A153189 Triangle T(n,k) = Product_{j=0..k} n*j+1.

Original entry on oeis.org

1, 1, 2, 1, 3, 15, 1, 4, 28, 280, 1, 5, 45, 585, 9945, 1, 6, 66, 1056, 22176, 576576, 1, 7, 91, 1729, 43225, 1339975, 49579075, 1, 8, 120, 2640, 76560, 2756160, 118514880, 5925744000, 1, 9, 153, 3825, 126225, 5175225, 253586025, 14454403425, 939536222625
Offset: 0

Views

Author

Roger L. Bagula, Dec 20 2008

Keywords

Comments

Row sums are: {1, 3, 19, 313, 10581, 599881, 50964103, 6047094369, 954249517513, 193146844030201, 48762935887310811,...}. [Corrected by M. F. Hasler, Oct 28 2014]
This is the lower left triangle of the array A142589. - M. F. Hasler, Oct 28 2014
Row n is a subset of the n-fold factorial sequence for k=0..n. For example, T(8,0..8) is A045755(1..9). These sequences are listed for n=0..10 in A256268. - Georg Fischer, Feb 15 2020

Examples

			Triangle begins as:
  1;
  1, 2;
  1, 3,  15;
  1, 4,  28,  280;
  1, 5,  45,  585,   9945;
  1, 6,  66, 1056,  22176,  576576;
  1, 7,  91, 1729,  43225, 1339975,  49579075;
  1, 8, 120, 2640,  76560, 2756160, 118514880,  5925744000;
  1, 9, 153, 3825, 126225, 5175225, 253586025, 14454403425, 939536222625;

Links

Crossrefs

Cf. A000165, A006882, A007661, A007662, A008544.
Cf. A000142 (row 2), A001147 (3), A007559 (4), A007696 (5), A008548 (6), A008542 (7), A045754 (8), A045755 (9), A045756 (10), A144773 (11), A256268 (combined table).

Programs

  • Magma
    [(&*[n*j+1: j in [0..k]]): k in [0..n], n in [0..10]]; // G. C. Greubel, Feb 15 2020
  • Maple
    seq(seq(mul(n*j+1, j=0..k), k=0..n), n=0..10); # G. C. Greubel, Feb 15 2020
  • Mathematica
    T[n_, k_]= If[n==0 && k==0, 1, Product[n*j+1, {j,0,k}]]; Table[T[n, k], {n,0,10}, {k,0,n}]//Flatten (* G. C. Greubel, Feb 15 2020 *)
T[n_, k_]:= T[n, k]= If[k<2, 1+k*n, ((1+n*k)*T[n, k-1] + (1+n*k)*(1+n*(k-1))* T[n, k-2])/2]; Table[T[n, k], {n,0,10}, {k,0,n}]//Flatten (* Georg Fischer, Feb 17 2020 *)
  • PARI
    T(n,k)=prod(j=0,k,n*j+1) \\ M. F. Hasler, Oct 28 2014
  • Sage
    [[ product(n*j+1 for j in (0..k)) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Feb 15 2020

Formula

T(n, k) = n^(k+1)*Pochhammer(1/n, k+1).
From Vaclav Kotesovec, Oct 10 2016: (Start)
For fixed n > 0:
T(n, k) ~ sqrt(2*Pi) * n^k * k^(k + 1/2 + 1/n) / (Gamma(1 + 1/n) * exp(k)).
T(n, k) ~ k! * n^k * k^(1/n) / Gamma(1 + 1/n).
(End)
T(n, k) = Sum_{j=0..k+1} (-1)^(k-j+1)*Stirling1(k+1,j)*n^(k-j+1). - G. C. Greubel, Feb 17 2020
T(n, k) = ((1+n*k)*T(n, k-1) + (1+n*k)*(1+n*(k-1))*T(n, k-2))/2. - Georg Fischer, Feb 17 2020

Extensions

Edited and row 0 added by M. F. Hasler, Oct 28 2014

A368119 Array read by ascending antidiagonals. A(n, k) = Product_{j=0..k-1} (n*j + 1).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 6, 1, 1, 1, 4, 15, 24, 1, 1, 1, 5, 28, 105, 120, 1, 1, 1, 6, 45, 280, 945, 720, 1, 1, 1, 7, 66, 585, 3640, 10395, 5040, 1, 1, 1, 8, 91, 1056, 9945, 58240, 135135, 40320, 1, 1, 1, 9, 120, 1729, 22176, 208845, 1106560, 2027025, 362880, 1
Offset: 0

Views

Author

Peter Luschny, Dec 18 2023

Keywords

Comments

A(n, k) is the number of increasing (n + 1)-ary trees on k vertices. (Following a comment of David Callan in A007559.)

Examples

			Array A(n, k) starts:
  [0] 1, 1, 1,   1,    1,      1,       1,         1, ...  A000012
  [1] 1, 1, 2,   6,   24,    120,     720,      5040, ...  A000142
  [2] 1, 1, 3,  15,  105,    945,   10395,    135135, ...  A001147
  [3] 1, 1, 4,  28,  280,   3640,   58240,   1106560, ...  A007559
  [4] 1, 1, 5,  45,  585,   9945,  208845,   5221125, ...  A007696
  [5] 1, 1, 6,  66, 1056,  22176,  576576,  17873856, ...  A008548
  [6] 1, 1, 7,  91, 1729,  43225, 1339975,  49579075, ...  A008542
  [7] 1, 1, 8, 120, 2640,  76560, 2756160, 118514880, ...  A045754
  [8] 1, 1, 9, 153, 3825, 126225, 5175225, 253586025, ...  A045755

Links

Crossrefs

Rows: A000012, A000142, A001147, A007559, A007696, A008548, A008542, A045754, A045755.
Columns: A000012, A000027, A000384, A011199, A011245.
Variant: A256268. Main diagonal: A092985.
Cf. A124320, A008279, A326323.

Programs

  • SageMath
    def A(n, k): return n**k * rising_factorial(1/n, k) if n > 0 else 1
for n in range(9): print([A(n, k) for k in range(8)])

Formula

Let rf(n, k) denote the rising factorial and ff(n,k) the falling factorial.
A(n, k) = n^k * rf(1/n, k) if n > 0 else 1.
A(n, k) = (-n)^k * ff(-1/n, k) if n > 0 else 1.
A(n, k) = (n^k * Gamma(k + 1/n)) / Gamma(1/n) for n > 0.
A(n, k) = ((-n)^k * Gamma(1 - 1/n)) / Gamma(1 - 1/n - k) for n > 0.
A(n, k) = k! * [x^k](1 - n*x)^(-1/n).
A(n, k) = [x^k] hypergeom([1, 1/n], [], n*x).
Column n + 1 has a linear recurrence with constant coefficients and signature ((-1)^k*binomial(n+1, n-k) for k=0..n).
Showing 1-8 of 8 results.

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