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 A016781 a(n) = (3*n+1)^5. 10
 1, 1024, 16807, 100000, 371293, 1048576, 2476099, 5153632, 9765625, 17210368, 28629151, 45435424, 69343957, 102400000, 147008443, 205962976, 282475249, 380204032, 503284375, 656356768, 844596301, 1073741824, 1350125107, 1680700000, 2073071593, 2535525376 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In general the e.g.f. of {(1 + 3*m)^n}_{m>=0} is E(n,x) = exp(x)*Sum_{m=0..n} A282629(n, m)*x^m, and the o.g.f. is G(n, x) = (Sum_{m=0..n} A225117(n, n-m}*x^m)/(1-x)^(n+1). - Wolfdieter Lang, Apr 02 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Harvey P. Dale, May 13 2012 From Wolfdieter Lang, Apr 02 2017: (Start) O.g.f.: (1+1018*x+10678*x^2+14498*x^3+2933*x^4+32*x^5)/(1-x)^6. E.g.f: exp(x)*(1+1023*x+7380*x^2+8775*x^3+2835*x^4+243*x^5). (End) a(n) = A000584(A016777(n)). - Michel Marcus, Apr 06 2017 Sum_{n>=0} 1/a(n) = 2*Pi^5/(3^6*sqrt(3)) + 121*zeta(5)/3^5. - Amiram Eldar, Mar 29 2022 MATHEMATICA (3Range[0, 20]+1)^5 (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 1024, 16807, 100000, 371293, 1048576}, 30] (* Harvey P. Dale, May 13 2012 *) PROG (Magma) [(3*n+1)^5: n in [0..30]]; // Vincenzo Librandi, Sep 21 2011 (Maxima) A016781(n):=(3*n+1)^5\$ makelist(A016781(n), n, 0, 20); /* Martin Ettl, Nov 12 2012 */ CROSSREFS Cf. A016777, A016778, A016779, A016780, A225117, A282629. Sequence in context: A138334 A268124 A205611 * A247933 A344306 A205349 Adjacent sequences: A016778 A016779 A016780 * A016782 A016783 A016784 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified February 8 08:49 EST 2023. Contains 360138 sequences. (Running on oeis4.)