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 A033593 a(n) = (n-1)*(2*n-1)*(3*n-1)*(4*n-1). 3
 1, 0, 105, 880, 3465, 9576, 21505, 42120, 74865, 123760, 193401, 288960, 416185, 581400, 791505, 1053976, 1376865, 1768800, 2238985, 2797200, 3453801, 4219720, 5106465, 6126120, 7291345, 8615376 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The sequence of n such that n is prime and (2*n+1) is prime is the sequence of Sophie Germain primes A005384; the subsequence of those for which in addition (3*n+2) is prime is A067256; and the subsequence of those for which in addition (4*n+3) is prime is A067257. - Jonathan Vos Post, Dec 15 2004 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA G.f.: (1 -5*x +115*x^2 +345*x^3 +120*x^4)/(1-x)^5. - R. J. Mathar, Jan 30 2011 From G. C. Greubel, Mar 05 2020: (Start) a(n) = n^4* Pochhammer((n-1)/n, 4). E.g.f.: (1 - x + 53*x^2 + 94*x^3 + 24*x^4)*exp(x). (End) MAPLE 1, seq( n^4*pochhammer((n-1)/n, 4), n=1..40); # G. C. Greubel, Mar 05 2020 MATHEMATICA Table[1-10 n+35 n^2-50 n^3+24 n^4, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 0, 105, 880, 3465}, 40]  (* Harvey P. Dale, Jan 29 2011 & Apr 26 2011 *) PROG (MAGMA) [ 24*n^4-50*n^3+35*n^2-10*n+1: n in [0..40]]; // Vincenzo Librandi, Jan 30 2011 (MAGMA) [&*[s*n-1: s in [1..4]]: n in [0..40]]; // Bruno Berselli, May 23 2011 (PARI) a(n)=24*n^4-50*n^3+35*n^2-10*n+1 \\ Charles R Greathouse IV, May 23 2011 (Sage) +[n^4*rising_factorial((n-1)/n, 4) for n in (1..40)] # G. C. Greubel, Mar 05 2020 CROSSREFS a(n) = A011245(-n). Cf. A005384, A033594, A067256, A067257. Sequence in context: A166816 A166798 A228303 * A297542 A266105 A058844 Adjacent sequences:  A033590 A033591 A033592 * A033594 A033595 A033596 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 5 03:52 EST 2021. Contains 349530 sequences. (Running on oeis4.)