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 A131509 a(n) = (n + 1)*(n^2 + 2)*(n^3 + 3)/6. 9
 1, 4, 33, 220, 1005, 3456, 9709, 23528, 50985, 101260, 187561, 328164, 547573, 877800, 1359765, 2044816, 2996369, 4291668, 6023665, 8303020, 11260221, 15047824, 19842813, 25849080, 33300025, 42461276, 53633529, 67155508, 83407045, 102812280, 125842981 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See also A131685(k) = smallest positive number m such that c(i) = m (i^1 + 1) (i^2 + 2) ... (i^k+ k) / k! takes integral values for all i>=0. For k=3, A131685(k)=1, which implies that this is a well defined integer sequence. - Alexander R. Povolotsky, May 18 2015 LINKS M. F. Hasler, Table of n, a(n) for n = 0..100 Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA G.f.: (1 -3x +26x^2 +38x^3 +53x^4 +5x^5)/(1-x)^7. - Emeric Deutsch, Aug 23 2007 MAPLE p:=proc(n, i) mul( n^j+j, j=1..i)/i!; end; [seq(p(n, 3), n=0..30)]; seq((1/6)*(n+1)*(n^2+2)*(n^3+3), n=0..25); # Emeric Deutsch, Aug 23 2007 MATHEMATICA Table[x = 3; Product[(n^k) + k, {k, x}]/6, {n, 0, 27}] (* Michael De Vlieger, Apr 24 2015 *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 4, 33, 220, 1005, 3456, 9709}, 40] (* Harvey P. Dale, Oct 18 2016 *) PROG (Maxima) A131509(n):=(n^1 + 1)*(n^2 + 2)*(n^3 + 3)/6\$ makelist(A131509(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */ (PARI) vector(20, n, n--; (n+1)*(n^2+2)*(n^3+3)/3!) \\ Derek Orr, Apr 25 2015 (MAGMA) [(n^1 + 1)*(n^2 + 2)*(n^3 + 3)/6: n in [0..30]]; // Vincenzo Librandi, Apr 25 2015 (PARI) A131509(n)=(n+1)*(n^2+2)*(n^3+3)/6 \\ M. F. Hasler, May 02 2015 CROSSREFS Cf. A000027 (k=1), A064808 (k=2), this sequence (k=3), A129995 (k=4), A131675 (k=5), ..., A131680 (k=10). Sequence in context: A273700 A273708 A097705 * A221030 A081007 A213168 Adjacent sequences:  A131506 A131507 A131508 * A131510 A131511 A131512 KEYWORD nonn,easy AUTHOR Alexander R. Povolotsky, Aug 13 2007, Aug 25 2007 EXTENSIONS Corrected and extended by R. J. Mathar and Emeric Deutsch, Aug 21 2007 STATUS approved

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Last modified December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)