A002397 a(n) = n! * lcm({1, 2, ..., n+1}). (Formerly M2036 N0807)

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

Offset

0,2

Comments

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

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]

Formula

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

Example

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

Prog

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

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.

Sequence in context: A002867 A235359 A130426 * A163085 A328946 A037515

Adjacent sequences: A002394 A002395 A002396 * A002398 A002399 A002400

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Nov 07 2013

More terms from Jack W Grahl, Feb 27 2021

Status

approved