A308363 a(n) = (1/n!) * Sum_{i_1=1..3} Sum_{i_2=1..3} ... Sum_{i_n=1..3} (-1)^(i_1 + i_2 + ... + i_n) * multinomial(i_1 + i_2 + ... + i_n; i_1, i_2, ..., i_n).

1, -1, 5, -120, 6286, -557991, 74741031, -14055359935, 3529670102365, -1140712320228976, 461095707510195836, -227895625979289345441, 135204234793000554759865, -94817763471081620680039785, 77590302489065260867070145321, -73270395178157034753637372218736

Offset: 0

Author

Seiichi Manyama, May 22 2019

Keywords

• sign

Examples

			a(2) = (1/2) * (binomial(1+1,1) - binomial(1+2,2) + binomial(1+3,3) - binomial(2+1,1) + binomial(2+2,2) - binomial(2+3,3) + binomial(3+1,1) - binomial(3+2,2) + binomial(3+3,3)) = 5.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..222

Crossrefs

Row n=3 of A308356.

Cf. A144416.

Programs

PARI

{a(n) = sum(i=n, 3*n, (-1)^i*i!*polcoef(sum(j=1, 3, x^j/j!)^n, i))/n!}