A308327
a(n) = (1/n!) * Sum_{i_1=1..n} Sum_{i_2=1..n} ... Sum_{i_n=1..n} (-1)^(i_1 + i_2 + ... + i_n) * multinomial(i_1 + i_2 + ... + i_n; i_1, i_2, ..., i_n).
Original entry on oeis.org
1, -1, 1, -120, 1056496, -2063348839223, 1457689055077930674637, -569779896381467292745562607320194, 174622933743914766946635359968704455433117668396, -56466564044341292662007179162722871704054012257606338926938133618
Offset: 0
a(2) = (1/2) * (binomial(1+1,1) - binomial(1+2,2) - binomial(2+1,1) + binomial(2+2,2)) = 1.
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{a(n) = sum(i=n, n^2, (-1)^i*i!*polcoef(sum(j=1, n, x^j/j!)^n, i))/n!}
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).
Original entry on oeis.org
1, -1, 5, -120, 6286, -557991, 74741031, -14055359935, 3529670102365, -1140712320228976, 461095707510195836, -227895625979289345441, 135204234793000554759865, -94817763471081620680039785, 77590302489065260867070145321, -73270395178157034753637372218736
Offset: 0
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.
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{a(n) = sum(i=n, 3*n, (-1)^i*i!*polcoef(sum(j=1, 3, x^j/j!)^n, i))/n!}
A308389
a(n) = (1/n!) * Sum_{i_1=1..4} Sum_{i_2=1..4} ... Sum_{i_n=1..4} (-1)^(i_1 + i_2 + ... + i_n) * multinomial(i_1 + i_2 + ... + i_n; i_1, i_2, ..., i_n).
Original entry on oeis.org
1, 0, 15, 2380, 1056496, 1006985994, 1762986495425, 5113595093793395, 22839265373518360690, 148735602883834110187329, 1353820891564948063221216616, 16652183007514287292261315076600, 269267286009015985660399792630965620, 5594310615550213586375706097295466365365
Offset: 0
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{a(n) = sum(i=n, 4*n, (-1)^i*i!*polcoef(sum(j=1, 4, x^j/j!)^n, i))/n!}
A308390
a(n) = (1/n!) * Sum_{i_1=1..5} Sum_{i_2=1..5} ... Sum_{i_n=1..5} (-1)^(i_1 + i_2 + ... + i_n) * multinomial(i_1 + i_2 + ... + i_n; i_1, i_2, ..., i_n).
Original entry on oeis.org
1, -1, 56, -52556, 197741887, -2063348839223, 48406314676155689, -2224972937386763396470, 181775891472021264149048031, -24546223741277444828277125708238, 5178698199109137849496232609026642706, -1632057854975794517762778147823325297971400
Offset: 0
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{a(n) = sum(i=n, 5*n, (-1)^i*i!*polcoef(sum(j=1, 5, x^j/j!)^n, i))/n!}
Showing 1-4 of 4 results.