A384029
a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)^4.
Original entry on oeis.org
1, 0, 6, 180, 7206, 370880, 23477380, 1768061064, 154544373158, 15387101825184, 1719596420272980, 213181689525888600, 29036623040055512332, 4310582688852993653568, 692756995680614782818992, 119830419866883597939018000, 22198322332579642585088580870, 4384714751330840129324051474880
Offset: 0
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a(n) = sum(i=0, n, sum(j=0, 3*n-i, sum(k=0, 3*n-i-j, abs(stirling(n, i, 1)*stirling(n, j, 1)*stirling(n, k, 1)*stirling(n, 3*n-i-j-k, 1)))));
A384026
a(n) = [x^(2*n)] Product_{k=0..n-1} (1 + k*x)^3.
Original entry on oeis.org
1, 0, 0, 8, 1188, 240480, 68630824, 26730127872, 13715719388784, 8994742935058880, 7351374493516431744, 7333037983443263351040, 8772990646534399559904256, 12403600039078715891159873280, 20464777911173655904724421045504, 38976211807455406964301439206318080
Offset: 0
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a(n) = sum(i=0, n, sum(j=0, n-i, abs(stirling(n, i, 1)*stirling(n, j, 1)*stirling(n, n-i-j, 1))));
A384089
a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)^n.
Original entry on oeis.org
1, 0, 1, 63, 7206, 1357300, 384271700, 153027592116, 81648987014364, 56259916067074896, 48646018448463951450, 51584263505394472459750, 65833976467770842558152992, 99553004175105699906002335098, 176031670802373999913671973955080, 359870756416991348769957239299854000
Offset: 0
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Table[SeriesCoefficient[Product[(1 + k*x)^n, {k, 0, n-1}], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, May 19 2025 *)
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a(n) = polcoef(prod(k=0, n-1, 1+k*x)^n, n);
Showing 1-3 of 3 results.