A002397 -id:A002397 - cp's OEIS frontend

A260781 Triangle read by rows: coefficients for corrector y(x_0) for step-by-step integration.

1, 1, 1, 5, 8, -1, 27, 57, -15, 3, 502, 1292, -528, 212, -38, 2375, 7135, -3990, 2410, -865, 135

Offset: 0

N. J. A. Sloane, Aug 02 2015

			Triangle begins:
1,
1,1,
5,8,-1,
27,57,-15,3,
502,1292,-528,212,-38,
2375,7135,-3990,2410,-865,135,
...

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] See Table III.

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

A360283 a(n) = lcm({n! * binomial(n, k) for k = 0..n}).

Original entry on oeis.org

1, 1, 4, 18, 288, 1200, 43200, 529200, 11289600, 91445760, 9144576000, 92207808000, 13277924352000, 160283515392000, 2094371267788800, 58904191906560000, 15079473128079360000, 242109318556385280000, 78443419212268830720000, 1415903716781452394496000

Offset: 0

Peter Luschny, Feb 14 2023

nonn

Cf. A002397, A003418 (LCM), A005722, A021012, A196347.

a := n -> ilcm(seq(n!*binomial(n, k), k=0..n)):
seq(a(n), n = 0..19);

from math import factorial, lcm
def A360283(n): return factorial(n)*lcm(*(i for i in range(1,n+2)))//(n+1) # Chai Wah Wu, Feb 15 2023

a(n) = n! * lcm({k for k = 1..n+1}) / (n+1) = n! * LCM(n + 1) / (n + 1).

a(n) / a(n-1) = n^2 if and only if n + 1 is prime, for n >= 1.

cp's OEIS Frontend

A260781 Triangle read by rows: coefficients for corrector y(x_0) for step-by-step integration.

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A360283 a(n) = lcm({n! * binomial(n, k) for k = 0..n}).

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