A002397 - OEIS

%I M2036 N0807 #43 Oct 15 2023 02:54:27

%S 1,2,12,72,1440,7200,302400,4233600,101606400,914457600,100590336000,

%T 1106493696000,172613016576000,2243969215488000,31415569016832000,

%U 942467070504960000,256351043177349120000,4357967734014935040000,1490424965033107783680000

%N a(n) = n! * lcm({1, 2, ..., n+1}).

%C This term appears in the numerator of several sequences of coefficients used in numerical solutions of ordinary differential equations.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Jack W Grahl, <a href="/A002397/b002397.txt">Table of n, a(n) for n = 0..100</a>

%H Jack W Grahl, <a href="/A002405/a002405.pdf">Explanation of the use of this sequence</a>.

%H Jack W Grahl, <a href="/A002405/a002405.py.txt">Python code to calculate this and related sequences</a>.

%H W. F. Pickard, <a href="https://doi.org/10.1145/321217.321226">Tables for the step-by-step integration of ordinary differential equations of the first order</a>, J. ACM 11 (1964), 229-233.

%H W. F. Pickard, <a href="/A002397/a002397.pdf">Tables for the step-by-step integration of ordinary differential equations of the first order</a>, J. ACM 11 (1964), 229-233. [Annotated scanned copy]

%F a(n) = n! * lcm{1,2,...,n+1} = n!*A003418(n+1). - _Sean A. Irvine_, Nov 07 2013

%e 5! is 120, and the least common multiple of 2, 3, 4, 5 and 6 is 60, so a(5) = 7200.

%o (PARI) a(n) = n!*lcm([1..n+1]); \\ _Michel Marcus_, Oct 15 2023

%Y Cf. A010796. Row sums of A260780, also of A260781.

%Y The following sequences are taken from page 231 of Pickard (1964): A002397, A002398, A002399, A002400, A002401, A002402, A002403, A002404, A002405, A002406, A260780, A260781.

%K nonn

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Nov 07 2013

%E More terms from _Jack W Grahl_, Feb 27 2021