A002397 a(n) = n! * lcm({1, 2, ..., n+1}).

1, 2, 12, 72, 1440, 7200, 302400, 4233600, 101606400, 914457600, 100590336000, 1106493696000, 172613016576000, 2243969215488000, 31415569016832000, 942467070504960000, 256351043177349120000, 4357967734014935040000, 1490424965033107783680000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

Examples

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

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Jack W Grahl, Table of n, a(n) for n = 0..100
• Jack W Grahl, Explanation of the use of this sequence.
• Jack W Grahl, Python code to calculate this and related sequences.
• W. F. Pickard, Tables for the step-by-step integration of ordinary differential equations of the first order, J. ACM 11 (1964), 229-233.
• W. F. Pickard, Tables for the step-by-step integration of ordinary differential equations of the first order, J. ACM 11 (1964), 229-233. [Annotated scanned copy]

Crossrefs

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

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

Programs

PARI

a(n) = n!*lcm([1..n+1]); \\ Michel Marcus, Oct 15 2023

Formula

a(n) = n! * lcm{1,2,...,n+1} = n!*A003418(n+1). - Sean A. Irvine, Nov 07 2013

Extensions

More terms from Sean A. Irvine, Nov 07 2013

More terms from Jack W Grahl, Feb 27 2021