

A033593


a(n) = (n1)*(2*n1)*(3*n1)*(4*n1).


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
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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)/(1x)^5.  R. J. Mathar, Jan 30 2011
From G. C. Greubel, Mar 05 2020: (Start)
a(n) = n^4* Pochhammer((n1)/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((n1)/n, 4), n=1..40); # G. C. Greubel, Mar 05 2020


MATHEMATICA

Table[110 n+35 n^250 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^450*n^3+35*n^210*n+1: n in [0..40]]; // Vincenzo Librandi, Jan 30 2011
(MAGMA) [&*[s*n1: s in [1..4]]: n in [0..40]]; // Bruno Berselli, May 23 2011
(PARI) a(n)=24*n^450*n^3+35*n^210*n+1 \\ Charles R Greathouse IV, May 23 2011
(Sage) [1]+[n^4*rising_factorial((n1)/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

N. J. A. Sloane


STATUS

approved



