A016795 -id:A016795 - cp's OEIS frontend

A016963 a(n) = (6*n + 4)^7.

16384, 10000000, 268435456, 2494357888, 13492928512, 52523350144, 163840000000, 435817657216, 1028071702528, 2207984167552, 4398046511104, 8235430000000, 14645194571776, 24928547056768, 40867559636992, 64847759419264, 100000000000000, 150363025899136, 221068140740608

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A016795, A016957, A016958, A016959, A016960, A016961, A016962.

Subsequence of A001015.

[(6*n+4)^7: n in [0..20]]; // Vincenzo Librandi, May 07 2011

(6*Range[0,20]+4)^7 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{16384,10000000,268435456,2494357888,13492928512,52523350144,163840000000,435817657216},20] (* Harvey P. Dale, Mar 03 2018 *)

From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016957(n)^7.
a(n) = 2^7*A016795(n).
Sum_{n>=0} 1/a(n) = 1093*zeta(7)/279936 - 7*Pi^7/(3149280*sqrt(3)). (End)

A016796 a(n) = (3*n + 2)^8.

Original entry on oeis.org

256, 390625, 16777216, 214358881, 1475789056, 6975757441, 25600000000, 78310985281, 208827064576, 500246412961, 1099511627776, 2251875390625, 4347792138496, 7984925229121, 14048223625216, 23811286661761, 39062500000000, 62259690411361, 96717311574016, 146830437604321

Offset: 0

N. J. A. Sloane

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Cf. A016789, A016790, A016791, A016792, A016793, A016794, A016795.

Subsequence of A001016.

(3 Range[0, 20] + 2)^8 (* Harvey P. Dale, Jan 24 2011 *)

From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016789(n)^6 = A016790(n)^3 = A016791(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(7, 2/3)/33067440. (End)

A016798 a(n) = (3*n + 2)^10.

Original entry on oeis.org

1024, 9765625, 1073741824, 25937424601, 289254654976, 2015993900449, 10240000000000, 41426511213649, 141167095653376, 420707233300201, 1125899906842624, 2758547353515625, 6278211847988224, 13422659310152401, 27197360938418176, 52599132235830049

Offset: 0

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A016789, A016790, A016791, A016792, A016793, A016794, A016795.

Subsequence of A008454.

(3*Range[0,20]+2)^10 (* Harvey P. Dale, Nov 28 2014 *)

From  Harvey P. Dale, Nov 28 2014: (Start)
G.f.: -(1/((x-1)^11))(x^10+1048565*x^9+270940968*x^8+6950443776*x^7+ 43221615834*x^6+86805830970*x^5+61387794480*x^4+14663204952*x^3+ 966376269*x^2+9754361*x+1024).
a(n) = 59049*n^10 + 393660*n^9 + 1180980*n^8 + 2099520*n^7 + 2449440*n^6 + 1959552*n^5 + 1088640*n^4 + 414720*n^3 + 103680*n^2 + 15360*n + 1024. [corrected by Amiram Eldar, Mar 31 2022] (End)
From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016789(n)^10 = A016790(n)^5 = A016793(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(9, 2/3)/21427701120. (End)
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11). - Wesley Ivan Hurt, Dec 31 2023

A016797 a(n) = (3*n + 2)^9.

Original entry on oeis.org

512, 1953125, 134217728, 2357947691, 20661046784, 118587876497, 512000000000, 1801152661463, 5429503678976, 14507145975869, 35184372088832, 78815638671875, 165216101262848, 327381934393961, 618121839509504, 1119130473102767, 1953125000000000, 3299763591802133

Offset: 0

N. J. A. Sloane

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Cf. A016789, A016790, A016791, A016792, A016793, A016794, A016795, A016796.

Subsequence of A001017.

Table[(3n+2)^9,{n,0,100}] (* Mohammad K. Azarian, Jun 15 2016 *)

G.f.: (512 + 1948005*x + 114709518*x^2 + 1103599596*x^3 + 2887100154*x^4 + 2388954618*x^5 + 608260290*x^6 + 37732212*x^7 + 262134*x^8 + x^9)/(1 - x)^10. - Ilya Gutkovskiy, Jun 16 2016
From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016789(n)^9.
Sum_{n>=0} 1/a(n) = 9841*zeta(9)/19683 - 1618*Pi^9/(55801305*sqrt(3)). (End)

A016799 a(n) = (3*n + 2)^11.

Original entry on oeis.org

2048, 48828125, 8589934592, 285311670611, 4049565169664, 34271896307633, 204800000000000, 952809757913927, 3670344486987776, 12200509765705829, 36028797018963968, 96549157373046875, 238572050223552512, 550329031716248441, 1196683881290399744, 2472159215084012303

Offset: 0

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Cf. A016789, A016790, A016791, A016792, A016793, A016794, A016795, A016796, A016797, A016798.

Subsequence of A008455.

(3Range[0,20]+2)^11 (* Harvey P. Dale, Apr 25 2011 *)

From Amiram Eldar, Apr 01 2022: (Start)
a(n) = A016789(n)^11.
Sum_{n>=0} 1/a(n) = 88573*zeta(11)/177147 - 7388*Pi^11/(2511058725*sqrt(3)). (End)

A016800 a(n) = (3*n + 2)^12.

Original entry on oeis.org

4096, 244140625, 68719476736, 3138428376721, 56693912375296, 582622237229761, 4096000000000000, 21914624432020321, 95428956661682176, 353814783205469041, 1152921504606846976, 3379220508056640625, 9065737908494995456, 22563490300366186081, 52654090776777588736

Offset: 0

N. J. A. Sloane

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Cf. A016789, A016790, A016791, A016792, A016793, A016794, A016795, A016796, A016797, A016798, A016799.

Subsequence of A008456.

Table[(3n+2)^12,{n,0,100}] (* Mohammad K. Azarian, Jun 15 2016 *)

From Amiram Eldar, Apr 01 2022: (Start)
a(n) = A016789(n)^12 = A016790(n)^6 = A016791(n)^4 = A016792(n)^3 = A016794(n)62.
Sum_{n>=0} 1/a(n) = PolyGamma(11, 2/3)/21213424108800. (End)

A017623 a(n) = (12*n + 8)^7.

Original entry on oeis.org

2097152, 1280000000, 34359738368, 319277809664, 1727094849536, 6722988818432, 20971520000000, 55784660123648, 131593177923584, 282621973446656, 562949953421312, 1054135040000000, 1874584905187328

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 (8,-28,56,-70,56,-28,8,-1).

Cf. A016795.

[(12*n+8)^7: n in [0..20]]; // Vincenzo Librandi, Aug 17 2011

(12*Range[0,15]+8)^7 (* Harvey P. Dale, Aug 16 2011 *)

vector(20, n, n--; (12*n+8)^7) \\ G. C. Greubel, Nov 08 2018

a(n) = 16384 * A016795(n). - R. J. Mathar, May 11 2008
G.f.: 16384*(x^7 + 16376*x^6 + 692499*x^5 + 3870352*x^4 + 4890287*x^3 + 1475736*x^2 + 77101*x + 128)/(x-1)^8. - Colin Barker, Aug 17 2012
E.g.f.: 16384*(128 +77997*x +970515*x^2 +2238327*x^3 +1655640*x^4 +479682*x^5 +56133*x^6 +2187*x^7)*exp(x). - G. C. Greubel, Nov 08 2018

cp's OEIS Frontend

A016963 a(n) = (6*n + 4)^7.

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A016796 a(n) = (3*n + 2)^8.

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A016798 a(n) = (3*n + 2)^10.

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A016797 a(n) = (3*n + 2)^9.

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A016799 a(n) = (3*n + 2)^11.

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A016800 a(n) = (3*n + 2)^12.

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A017623 a(n) = (12*n + 8)^7.

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