A016763 -id:A016763 - cp's OEIS frontend

A016751 a(n) = (2*n)^11.

0, 2048, 4194304, 362797056, 8589934592, 100000000000, 743008370688, 4049565169664, 17592186044416, 64268410079232, 204800000000000, 584318301411328, 1521681143169024, 3670344486987776, 8293509467471872, 17714700000000000, 36028797018963968, 70188843638032384

Offset: 0

N. J. A. Sloane

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. A016763.

[(2*n)^11: n in [0..20]]; // Vincenzo Librandi, Sep 05 2011

A016751:=n->(2*n)^11: seq(A016751(n), n=0..30); # Wesley Ivan Hurt, Sep 15 2018

Table[(2*n)^11, {n,0,30}] (* G. C. Greubel, Sep 15 2018 *)

vector(30, n, n--; (2*n)^11) \\ G. C. Greubel, Sep 15 2018

G.f.: 2048*x*(1 + 2036*x + 152637*x^2 + 2203488*x^3 + 9738114*x^4 + 15724248*x^5 + 9738114*x^6 + 2203488*x^7 + 152637*x^8 + 2036*x^9 + x^10)/(x-1)^12. - R. J. Mathar, Jul 07 2017
From Amiram Eldar, Oct 11 2020: (Start)
Sum_{n>=1} 1/a(n) = zeta(11)/2048.
Sum_{n>=1} (-1)^(n+1)/a(n) = 1023*zeta(11)/2097152. (End)

A016955 a(n) = (6*n + 3)^11.

Original entry on oeis.org

177147, 31381059609, 8649755859375, 350277500542221, 5559060566555523, 50542106513726817, 317475837322472439, 1532278301220703125, 6071163615208263051, 20635899893042801193, 62050608388552823487, 168787390185178426269, 422351360321044921875, 984770902183611232881

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Cf. A016763, A016945, A016946, A016947, A016948, A016949, A016950, A016951, A016952, A016953, A016954.

Subsequence of A008455.

[(6*n+3)^11: n in [0..20]]; // Vincenzo Librandi, May 06 2011

a[n_] := (6*n + 3)^11; Array[a, 50, 0] (* Amiram Eldar, Mar 30 2022 *)

From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016945(n)^11.
a(n) = 3^11*A016763(n).
Sum_{n>=0} 1/a(n) = 2047*zeta(11)/362797056.
Sum_{n>=0} (-1)^n/a(n) = 50521*Pi^11/2633035913625600. (End)

A016835 a(n) = (4n+2)^11.

Original entry on oeis.org

2048, 362797056, 100000000000, 4049565169664, 64268410079232, 584318301411328, 3670344486987776, 17714700000000000, 70188843638032384, 238572050223552512, 717368321110468608, 1951354384207722496, 4882812500000000000, 11384956040305711104, 24986644000165537792

Offset: 0

N. J. A. Sloane

Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Cf. A013669, A016763, A016825.

Table[(4*n+2)^11, {n, 0, 20}] (* Amiram Eldar, Apr 21 2023 *)

From Amiram Eldar, Apr 21 2023: (Start)
a(n) = A016825(n)^11.
a(n) = 2^11*A016763(n).
Sum_{n>=0} 1/a(n) = 2047*zeta(11)/4194304.
Sum_{n>=0} (-1)^n/a(n) = 50521*Pi^11/30440580710400. (End)

A017123 a(n) = (8*n + 4)^11.

Original entry on oeis.org

4194304, 743008370688, 204800000000000, 8293509467471872, 131621703842267136, 1196683881290399744, 7516865509350965248, 36279705600000000000, 143746751770690322432, 488595558857835544576, 1469170321634239709184, 3996373778857415671808, 10000000000000000000000

Offset: 0

N. J. A. Sloane

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. A013669, A016763, A016835, A017113.

[(8*n+4)^11: n in [0..15] ]; // Vincenzo Librandi, Jul 21 2011

(8*Range[0,20]+4)^11 (* Harvey P. Dale, Jun 11 2016 *)

G.f.: ( 4194304*(1+x)*(x^10 + 177134*x^9 + 46525293*x^8 + 1356555432*x^7 + 9480267666*x^6 + 19107752148*x^5 + 9480267666*x^4 + 1356555432*x^3 + 46525293*x^2 + 177134*x+1) ) / ( (x-1)^12 ). - R. J. Mathar, May 08 2015
From Amiram Eldar, Apr 25 2023: (Start)
a(n) = A017113(n)^11.
a(n) = 2^11*A016835(n) = 2^22*A016763(n).
Sum_{n>=0} 1/a(n) = 2047*zeta(11)/8589934592.
Sum_{n>=0} (-1)^n/a(n) = 50521*Pi^11/62342309294899200. (End)

A017339 a(n) = (10*n + 5)^11.

Original entry on oeis.org

48828125, 8649755859375, 2384185791015625, 96549157373046875, 1532278301220703125, 13931233916552734375, 87507831740087890625, 422351360321044921875, 1673432436896142578125, 5688000922764599609375, 17103393581163134765625, 46523913960640966796875, 116415321826934814453125

Offset: 0

N. J. A. Sloane

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. A013669, A016763, A017329.

[(10*n+5)^11: n in [0..10]]; // Vincenzo Librandi, Aug 02 2011

Table[(10*n + 5)^11, {n, 0, 15}] (* Amiram Eldar, Apr 18 2023 *)

G.f.: 48828125*(x+1)*(x^10 + 177134*x^9 + 46525293*x^8 + 1356555432*x^7 + 9480267666*x^6 + 19107752148*x^5 + 9480267666*x^4 + 1356555432*x^3 + 46525293*x^2 + 177134*x + 1)/(x-1)^12. - Colin Barker, Nov 14 2012
From Amiram Eldar, Apr 18 2023: (Start)
a(n) = A017329(n)^11.
a(n) = 5^11 * A016763(n).
Sum_{n>=0} 1/a(n) = 2047*zeta(11)/100000000000.
Sum_{n>=0} (-1)^n/a(n) = 50521*Pi^11/725760000000000000. (End)

cp's OEIS Frontend

A016751 a(n) = (2*n)^11.

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A016955 a(n) = (6*n + 3)^11.

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A016835 a(n) = (4n+2)^11.

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A017123 a(n) = (8*n + 4)^11.

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A017339 a(n) = (10*n + 5)^11.

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