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A016781
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a(n) = (3*n+1)^5.
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10
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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FORMULA
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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
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)
Sum_{n>=0} 1/a(n) = 2*Pi^5/(3^6*sqrt(3)) + 121*zeta(5)/3^5. - Amiram Eldar, Mar 29 2022
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MATHEMATICA
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(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 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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