A170793 -id:A170793 - cp's OEIS frontend

A170798 a(n) = n^10*(n^6 + 1)/2.

0, 1, 33280, 21552885, 2148007936, 76298828125, 1410585186816, 16616606522425, 140738025226240, 926511837818121, 5000005000000000, 22974877900498381, 92442160406200320, 332708373520835845, 1088976813532013056

Offset: 0

N. J. A. Sloane, Dec 11 2009

a(n) is number of distinct 4 X 4 matrices with entries in {1,2,...,n} when a matrix and its transpose are considered equivalent. - David Nacin, Feb 20 2017

Cycle index of this S2 group action is (s(2)^6s(1)^4+s(1)^16)/2. - David Nacin, Feb 20 2017

			a(2) = 33280 is the number of inequivalent 4 X 4 binary matrices up to taking the transpose. - _David Nacin_, Feb 20 2017

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), A170796 (m=4), A170797 (m=5), this sequence (m=6), A170799 (m=7), A170800 (m=8), A170801 (m=9), A170802 (m=10).

List([0..20], n-> n^10*(n^6 +1)/2); # G. C. Greubel, Oct 11 2019

[n^10*(n^6+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

seq(n^10*(n^6+1)/2, n=0..20); # G. C. Greubel, Oct 12 2019

Table[n^10*(n^6+1)/2,{n,0,30}] (* Harvey P. Dale, Aug 27 2016 *)

concat(0, Vec(-x*(x +1)*(x^14 +33262*x^13 +20953999*x^12 +1765180292*x^11 +40926077261*x^10 +350131349138*x^9 +1253612167971*x^8 +1937785948152*x^7 +1253612167971*x^6 +350131349138*x^5 +40926077261*x^4 +1765180292*x^3 +20953999*x^2 +33262*x +1) / (x -1)^17 + O(x^30))) \\ Colin Barker, Jul 11 2015

vector(21, m, (m-1)^10*((m-1)^6 + 1)/2) \\ G. C. Greubel, Oct 11 2019

[n^10*(n^6 +1)/2 for n in (0..20)] # G. C. Greubel, Oct 11 2019

G.f.: x*(x+1)*(x^14 + 33262*x^13 + 20953999*x^12 + 1765180292*x^11 + 40926077261*x^10 + 350131349138*x^9 + 1253612167971*x^8 + 1937785948152*x^7 + 1253612167971*x^6 + 350131349138*x^5 + 40926077261*x^4 + 1765180292*x^3 + 20953999*x^2 + 33262*x + 1)/(1-x)^17. - Colin Barker, Jul 11 2015

E.g.f.: x*(2 + 33278*x + 7151016*x^2 + 171833006*x^3 + 1096233075*x^4 + 2734949385*x^5 + 3281888484*x^6 + 2141764803*x^7 + 820784295*x^8 + 193754991*x^9 + 28936908*x^10 + 2757118*x^11 + 165620*x^12 + 6020*x^13 + 120*x^14 + x^15)*exp(x)/2. - G. C. Greubel, Oct 12 2019

A170801 a(n) = n^10*(n^9 + 1)/2.

Original entry on oeis.org

0, 1, 262656, 581160258, 137439477760, 9536748046875, 304679900238336, 5699447733924196, 72057594574798848, 675425860579888245, 5000000005000000000, 30579545237175985446, 159739999716270145536

Offset: 0

N. J. A. Sloane, Dec 11 2009

Number of unoriented rows of length 19 using up to n colors. For a(0)=0, there are no rows using no colors. For a(1)=1, there is one row using that one color for all positions. For a(2)=262656, there are 2^19=524288 oriented arrangements of two colors. Of these, 2^10=1024 are achiral. That leaves (524288-1024)/2=261632 chiral pairs. Adding achiral and chiral, we get 262656. - Robert A. Russell, Nov 13 2018

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (20, -190, 1140, -4845, 15504, -38760, 77520, -125970, 167960, -184756, 167960, -125970, 77520, -38760, 15504, -4845, 1140, -190, 20, -1).

Row 19 of A277504.
Cf. A010807 (oriented), A008454 (achiral).
Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), A170796 (m=4), A170797 (m=5), A170798 (m=6), A170799 (m=7), A170800 (m=8), this sequence (m=9), A170802 (m=10).

List([0..30], n -> n^10*(n^9+1)/2); # G. C. Greubel, Nov 15 2018

[n^10*(n^9+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

seq(n^10*(n^9 +1)/2, n=0..20); # G. C. Greubel, Oct 11 2019

Table[(n^19 + n^10)/2, {n,0,30}] (* Robert A. Russell, Nov 13 2018 *)

vector(30, n, n--; n^10*(n^9+1)/2) \\ G. C. Greubel, Nov 15 2018

[n^10*(n^9+1)/2 for n in range(30)] # G. C. Greubel, Nov 15 2018

From Robert A. Russell, Nov 13 2018: (Start)
a(n) = (A010807(n) + A008454(n)) / 2 = (n^19 + n^10) / 2.
G.f.: (Sum_{j=1..19} S2(19,j)*j!*x^j/(1-x)^(j+1) + Sum_{j=1..10} S2(10,j)*j!*x^j/(1-x)^(j+1)) / 2, where S2 is the Stirling subset number A008277.
G.f.: x*Sum_{k=0..18} A145882(19,k) * x^k / (1-x)^20.
E.g.f.: (Sum_{k=1..19} S2(19,k)*x^k + Sum_{k=1..10} S2(10,k)*x^k) * exp(x) / 2, where S2 is the Stirling subset number A008277.
For n>19, a(n) = Sum_{j=1..20} -binomial(j-21,j) * a(n-j). (End)

A170802 a(n) = n^10*(n^10 + 1)/2.

Original entry on oeis.org

0, 1, 524800, 1743421725, 549756338176, 47683720703125, 1828079250264576, 39896133290043625, 576460752840294400, 6078832731271856601, 50000000005000000000, 336374997479248716901, 1916879996254696243200

Offset: 0

N. J. A. Sloane, Dec 11 2009

By definition, all terms are triangular numbers. - Harvey P. Dale, Aug 12 2012

Number of unoriented rows of length 20 using up to n colors. For a(0)=0, there are no rows using no colors. For a(1)=1, there is one row using that one color for all positions. For a(2)=524800, there are 2^20=1048576 oriented arrangements of two colors. Of these, 2^10=1024 are achiral. That leaves (1048576-1024)/2=523776 chiral pairs. Adding achiral and chiral, we get 524800. - Robert A. Russell, Nov 13 2018

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).

Row 20 of A277504.
Cf. A010808 (oriented), A008454 (achiral).
Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), A170896 (m=4), A170797 (m=5), A170798 (m=6), A170799 (m=7), A170800 (m=8), A170801 (m=9), this sequence (m=10).

List([0..30], n -> n^10*(n^10+1)/2); # G. C. Greubel, Nov 15 2018

[n^10*(n^10+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

seq(n^10*(n^10 +1)/2, n=0..20); # G. C. Greubel, Oct 11 2019

n10[n_]:=Module[{c=n^10},(c(c+1))/2];Array[n10,15,0] (* Harvey P. Dale, Jul 17 2012 *)

vector(30, n, n--; n^10*(n^10+1)/2) \\ G. C. Greubel, Nov 15 2018

for n in range(0,20): print(int(n**10*(n**10 + 1)/2), end=', ') # Stefano Spezia, Nov 15 2018

[n^10*(n^10+1)/2 for n in range(30)] # G. C. Greubel, Nov 15 2018

From Robert A. Russell, Nov 13 2018: (Start)
a(n) = (A010808(n) + A008454(n)) / 2 = (n^20 + n^10) / 2.
G.f.: (Sum_{j=1..20} S2(20,j)*j!*x^j/(1-x)^(j+1) + Sum_{j=1..10} S2(10,j)*j!*x^j/(1-x)^(j+1)) / 2, where S2 is the Stirling subset number A008277.
G.f.: x*Sum_{k=0..19} A145882(20,k) * x^k / (1-x)^21.
E.g.f.: (Sum_{k=1..20} S2(20,k)*x^k + Sum_{k=1..10} S2(10,k)*x^k) * exp(x) / 2, where S2 is the Stirling subset number A008277.
For n>20, a(n) = Sum_{j=1..21} -binomial(j-22,j) * a(n-j). (End)

A170797 a(n) = n^10*(n^5+1)/2.

Original entry on oeis.org

0, 1, 16896, 7203978, 537395200, 15263671875, 235122725376, 2373921992596, 17592722915328, 102947309439525, 500005000000000, 2088637053420126, 7703541745975296, 25593015436291303, 77784192406233600

Offset: 0

N. J. A. Sloane, Dec 11 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), A170796 (m=4), this sequence (m=5), A170798 (m=6), A170799 (m=7), A170800 (m=8), A170801 (m=9), A170802 (m=10).

List([0..20], n-> n^10*(n^5 +1)/2); # G. C. Greubel, Oct 11 2019

[n^10*(n^5+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 26 2011

A170797:=n->n^10*(n^5+1)/2: seq(A170797(n), n=0..20); # Wesley Ivan Hurt, Aug 10 2016

Table[n^10*(n^5 + 1)/2, {n, 0, 15}] (* Wesley Ivan Hurt, Aug 10 2016 *)

vector(21, m, (m-1)^10*((m-1)^5 + 1)/2) \\ G. C. Greubel, Oct 11 2019

[n^10*(n^5 +1)/2 for n in (0..20)] # G. C. Greubel, Oct 11 2019

G.f.: x*(15872*x^13 +6890977*x^12 +423932400*x^11 +7520863426*x^10 +51389080880*x^9 +155692452591*x^8 +223769408736*x^7 +155695145820*x^6 +51387918048*x^5 +7520366095*x^4 +424158512*x^3 +6933762*x^2 +16880*x +1) / (x-1)^16. - Colin Barker, Nov 01 2014
a(n) = 16*a(n-1) - 120*a(n-2) + 560*a(n-3) - 1820*a(n-4) + 4368*a(n-5) - 8008*a(n-6) + 11440*a(n-7) - 12870*a(n-8) + 11440*a(n-9) - 8008*a(n-10) + 4368*a(n-11) - 1820*a(n-12) + 560*a(n-13) - 120*a(n-14) + 16*a(n-15) - a(n-16) for n > 15. - Wesley Ivan Hurt, Aug 10 2016
E.g.f.: x*(2 +16894*x +2384431*x^2 +42390055*x^3 +210809445*x^4 + 420716100*x^5 +408747213*x^6 +216628590*x^7 +67128535*x^8 +12662651*x^9 +1479478*x^10 +106470*x^11 +4550*x^12 +105*x^13 +x^14)*exp(x)/2. - G. C. Greubel, Oct 11 2019

A170799 a(n) = n^10*(n^7 + 1)/2.

Original entry on oeis.org

0, 1, 66048, 64599606, 8590458880, 381474609375, 8463359955456, 116315398231228, 1125900443713536, 8338592593225485, 50000005000000000, 252723527218359186, 1109305584328900608, 4325208028619914891, 15245673509292925440, 49263062956171875000, 147573953139432226816

Offset: 0

N. J. A. Sloane, Dec 11 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).

Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), A170796 (m=4), A170797 (m=5), A170798 (m=6), this sequence (m=7), A170800 (m=8), A170801 (m=9), A170802 (m=10).

List([0..20], n-> n^10*(n^7 +1)/2); # G. C. Greubel, Oct 11 2019

[n^10*(n^7+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

seq(n^10*(n^7 +1)/2, n=0..20); # G. C. Greubel, Oct 11 2019

Table[n^10(n^7+1)/2,{n,0,20}] (* Harvey P. Dale, Aug 27 2013 *)

vector(21, m, (m-1)^10*((m-1)^7 + 1)/2) \\ G. C. Greubel, Oct 11 2019

[n^10*(n^7 +1)/2 for n in (0..20)] # G. C. Greubel, Oct 11 2019

G.f.: x*(65024*x^15 + 63370125*x^14 + 7437628950*x^13 + 236677103915*x^12 + 2858645957220*x^11 + 15527824213413*x^10 + 41568614867330*x^9 + 57445190329275*x^8 + 41568608318040*x^7 + 15527828734975*x^6 + 2858646015162*x^5 + 236676197145*x^4 + 7437770500*x^3 + 63410895*x^2 + 66030*x + 1)/(x-1)^18. - Colin Barker, Feb 24 2013

E.g.f.: x*(2 + 66046*x + 21467155*x^2 + 694371395*x^3 + 5652794176*x^4 + 17505772725*x^5 + 25708110666*x^6 + 20415995778*x^7 + 9528822348*x^8 + 2758334151*x^9 + 512060978*x^10 + 62022324*x^11 + 4910178*x^12 + 249900*x^13 + 7820*x^14 + 136*x^15 + x^16)*exp(x)/2. - G. C. Greubel, Oct 12 2019

A170800 a(n) = n^10*(n^8 + 1)/2.

Original entry on oeis.org

0, 1, 131584, 193739769, 34360262656, 1907353515625, 50780008567296, 814206940192849, 9007199791611904, 75047319391891761, 500000005000000000, 2779958669714828041, 13311666671401304064, 56227703544907942489

Offset: 0

N. J. A. Sloane, Dec 11 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (19,-171,969,-3876,11628,-27132,50388,-75582,92378,-92378,75582,-50388,27132,-11628,3876,-969,171,-19,1).

Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), A170796 (m=4), A170797 (m=5), A170798 (m=6), A170799 (m=7), this sequence (m=8), A170801 (m=9), A170802 (m=10).

List([0..20], n-> n^10*(n^8 +1)/2); # G. C. Greubel, Oct 11 2019

[n^10*(n^8+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

seq(n^10*(n^8 +1)/2, n=0..20); # G. C. Greubel, Oct 11 2019

Table[n^10 (n^8+1)/2,{n,0,20}] (* Harvey P. Dale, Jul 14 2013 *)

vector(21, m, (m-1)^10*((m-1)^8 + 1)/2) \\ G. C. Greubel, Oct 11 2019

[n^10*(n^8 +1)/2 for n in (0..20)] # G. C. Greubel, Oct 11 2019

G.f.: x*(1 + 131565*x + 191239844*x^2 + 30701706940*x^3 + 1287510524640*x^4 + 20228672856392*x^5 + 142998539385460*x^6 + 503354978422188*x^7 + 932692832164970*x^8 + 932692832164970*x^9 + 503354978422188*x^10 + 142998539385460*x^11 + 20228672856392*x^12 + 1287510524640*x^13 + 30701706940*x^14 +191239844*x^15 + 131565*x^16 + x^17)/(1-x)^19. - Harvey P. Dale, Jul 14 2013

E.g.f.: x*(2 + 131582*x + 64448340*x^2 + 2798841090*x^3 + 28958138070*x^4 + 110687273866*x^5 + 197462489280*x^6 + 189036065760*x^7 + 106175395800*x^8 + 37112163804*x^9 + 8391004908*x^10 + 1256328866*x^11 + 125854638*x^12 + 8408778*x^13 + 367200*x^14 + 9996*x^15 + 153*x^16 + x^17)*exp(x)/2. - G. C. Greubel, Oct 12 2019

A170796 a(n) = n^10*(n^4 + 1)/2.

Original entry on oeis.org

0, 1, 8704, 2421009, 134742016, 3056640625, 39212315136, 339252774049, 2199560126464, 11440139619681, 50005000000000, 189887885503921, 641990190956544, 1968757122095569, 5556148040106496, 14596751337890625

Offset: 0

N. J. A. Sloane, Dec 11 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), this sequence (m=4), A170797 (m=5), A170798 (m=6), A170799 (m=7), A170800 (m=8), A170801 (m=9), A170802 (m=10).

List([0..20], n-> n^10*(n^4 +1)/2); # G. C. Greubel, Oct 11 2019

[n^10*(n^4+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 26 2011

seq(n^10*(n^4 +1)/2, n=0..20); # G. C. Greubel, Oct 11 2019

Table[n^10*(n^4 +1)/2, {n,0,20}] (* G. C. Greubel, Oct 11 2019 *)

vector(21, m, (m-1)^10*((m-1)^4 + 1)/2) \\ G. C. Greubel, Oct 11 2019

[n^10*(n^4 +1)/2 for n in (0..20)] # G. C. Greubel, Oct 11 2019

From G. C. Greubel, Oct 11 2019: (Start)
G.f.: x*(1 +8689*x +2290554*x^2 +99340346*x^3 +1285757375*x^4 +6420936303*x^5 +13986239532*x^6 +13986239532*x^7 +6420936303*x^8 +1285757375*x^9 +99340346*x^10 +2290554*x^11 +8689*x^12 +x^13)/(1-x)^15.
E.g.f.: x*(2 +8702*x +798300*x^2 +10425850*x^3 +40117560*x^4 +63459200*x^5 +49335160*x^6 +20913070*x^7 +5135175*x^8 +752753*x^9 + 66066*x^10 +3367*x^11 +91*x^12 +x^13)*exp(x)/2. (End)

A158497 Triangle T(n,k) formed by the coordination sequences and the number of leaves for trees.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 3, 6, 12, 1, 4, 12, 36, 108, 1, 5, 20, 80, 320, 1280, 1, 6, 30, 150, 750, 3750, 18750, 1, 7, 42, 252, 1512, 9072, 54432, 326592, 1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890

Offset: 0

Thomas Wieder, Mar 20 2009

Consider the k-fold Cartesian products CP(n,k) of the vector A(n) = [1, 2, 3, ..., n].
An element of CP(n,k) is a n-tuple T_t of the form T_t = [i_1, i_2, i_3, ..., i_k] with t=1, .., n^k.
We count members T of CP(n,k) which satisfy some condition delta(T_t), so delta(.) is an indicator function which attains values of 1 or 0 depending on whether T_t is to be counted or not; the summation sum_{CP(n,k)} delta(T_t) over all elements T_t of CP produces the count.
For the triangle here we have delta(T_t) = 0 if for any two i_j, i_(j+1) in T_t one has i_j = i_(j+1): T(n,k) = Sum_{CP(n,k)} delta(T_t) = Sum_{CP(n,k)} delta(i_j = i_(j+1)).
The test on i_j > i_(j+1) generates A158498. One gets the Pascal triangle A007318 if the indicator function tests whether for any two i_j, i_(j+1) in T_t one has i_j >= i_(j+1).
Use of other indicator functions can also calculate the Bell numbers A000110, A000045 or A000108.

			Array, A(n, k) = n*(n-1)^(k-1) for n > 1, A(n, k) = 1 otherwise, begins as:
  1,  1,   1,    1,     1,      1,       1,        1,        1, ... A000012;
  1,  1,   1,    1,     1,      1,       1,        1,        1, ... A000012;
  1,  2,   2,    2,     2,      2,       2,        2,        2, ... A040000;
  1,  3,   6,   12,    24,     48,      96,      192,      384, ... A003945;
  1,  4,  12,   36,   108,    324,     972,     2916,     8748, ... A003946;
  1,  5,  20,   80,   320,   1280,    5120,    20480,    81920, ... A003947;
  1,  6,  30,  150,   750,   3750,   18750,    93750,   468750, ... A003948;
  1,  7,  42,  252,  1512,   9072,   54432,   326592,  1959552, ... A003949;
  1,  8,  56,  392,  2744,  19208,  134456,   941192,  6588344, ... A003950;
  1,  9,  72,  576,  4608,  36864,  294912,  2359296, 18874368, ... A003951;
  1, 10,  90,  810,  7290,  65610,  590490,  5314410, 47829690, ... A003952;
  1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, ............. A003953;
  1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, ............. A003954;
  1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, ............. A170732;
  ... ;
The triangle begins as:
  1
  1, 1;
  1, 2,  2;
  1, 3,  6,  12;
  1, 4, 12,  36,  108;
  1, 5, 20,  80,  320,  1280;
  1, 6, 30, 150,  750,  3750,  18750;
  1, 7, 42, 252, 1512,  9072,  54432, 326592;
  1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344;
  ...;
T(3,3) = 12 counts the triples (1,2,1), (1,2,3), (1,3,1), (1,3,2), (2,1,2), (2,1,3), (2,3,1), (2,3,2), (3,1,2), (3,1,3), (3,2,1), (3,2,3) out of a total of 3^3 = 27 triples in the CP(3,3).

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

Array rows n: A170733 (n=14), ..., A170769 (n=50).
Columns k: A000012(n) (k=0), A000027(n) (k=1), A002378(n-1) (k=2), A011379(n-1) (k=3), A179824(n) (k=4), A101362(n-1) (k=5), 2*A168351(n-1) (k=6), 2*A168526(n-1) (k=7), 2*A168635(n-1) (k=8), 2*A168675(n-1) (k=9), 2*A170783(n-1) (k=10), 2*A170793(n-1) (k=11).
Diagonals k: A055897 (k=n), A055541 (k=n-1), A373395 (k=n-2), A379612 (k=n-3).
Sums: (-1)^n*A065440(n) (signed row).
Cf. A000045, A000108, A000110, A007318, A079901, A158498.

A158497:= func< n,k | k le 1 select n^k else n*(n-1)^(k-1) >;
[A158497(n,k): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 18 2025

A158497[n_, k_]:= If[n<2 || k==0, 1, n*(n-1)^(k-1)];
Table[A158497[n,k], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Mar 18 2025 *)

def A158497(n,k): return n^k if k<2 else n*(n-1)^(k-1)
print(flatten([[A158497(n,k) for k in range(n+1)] for n in range(13)])) # G. C. Greubel, Mar 18 2025

T(n, k) = (n-1)^(k-1) + (n-1)^k = n*A079901(n-1,k-1), k > 0.

Sum_{k=0..n} T(n,k) = (n*(n-1)^n - 2)/(n-2), n > 2.

Edited by R. J. Mathar, Mar 31 2009

More terms added by G. C. Greubel, Mar 18 2025

A168119 n*(n^10+1)/2.

Original entry on oeis.org

0, 1, 1025, 88575, 2097154, 24414065, 181398531, 988663375, 4294967300, 15690529809, 50000000005, 142655835311, 371504185350, 896080197025, 2024782584839, 4324877929695, 8796093022216, 17135948153825

Offset: 0

N. J. A. Sloane, Dec 11 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Cf. A170793.

[n*(n^10+1)/2: n in [0..20]]; // Vincenzo Librandi, Sep 15 2011

Table[n (n^10 + 1)/2, {n, 0, 20}] (* Harvey P. Dale, Sep 14 2011 *)
CoefficientList[Series[x (1 + 1013 x + 76341 x^2 + 1101684 x^3 + 4869162 x^4 + 7861998 x^5 + 4869162 x^6 + 1101684 x^7 + 76341 x^8 + 1013 x^9 + x^10)/(1 - x)^12, {x, 0, 20}], x] (* Vincenzo Librandi, Dec 10 2014 *)

G.f.: x*(1 + 1013*x + 76341*x^2 + 1101684*x^3 + 4869162*x^4 + 7861998*x^5 + 4869162*x^6 + 1101684*x^7 + 76341*x^8 + 1013*x^9 + x^10)/(1 - x)^12. - Vincenzo Librandi, Dec 10 2014

cp's OEIS Frontend

A170798 a(n) = n^10*(n^6 + 1)/2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

PARI

Sage

Formula

A170801 a(n) = n^10*(n^9 + 1)/2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

A170802 a(n) = n^10*(n^10 + 1)/2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Python

Sage

Formula

A170797 a(n) = n^10*(n^5+1)/2.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

A170799 a(n) = n^10*(n^7 + 1)/2.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

A170800 a(n) = n^10*(n^8 + 1)/2.

Views

Author