A351507
a(n) = [x^n] Product_{k=1..n} (1 + k*x)^n.
Original entry on oeis.org
1, 1, 13, 630, 65446, 11732175, 3222746276, 1257489289280, 661150527657180, 450529025613124095, 386183537239831846450, 406654820487854059966416, 516014868401631381045209376, 776565429016998902169538130936, 1367544537916924083498367095477800
Offset: 0
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Table[SeriesCoefficient[Product[(1 + k*x)^n, {k,1,n}], {x,0,n}], {n,0,20}] (* Vaclav Kotesovec, Feb 18 2022 *)
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a(n) = polcoef(prod(k=1, n, 1+k*x)^n, n);
A351764
a(n) = [x^n] Product_{k=1..n} (1 + k*x)^n / (1 - k*x)^n.
Original entry on oeis.org
1, 2, 72, 7848, 1728000, 641258850, 360403076376, 285818177146208, 304172586944446464, 418400927094822149970, 722587619114932445325000, 1530927286486636135080191736, 3904621941927926455303092180480, 11801667653769333351640692783069714
Offset: 0
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Table[SeriesCoefficient[Product[(1 + k*x)^n / (1 - k*x)^n, {k,1,n}], {x,0,n}], {n,0,20}]
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a(n) = my(x='x+O(x^(n+1))); polcoef(prod(k=1, n, (1+k*x)^n/ (1-k*x)^n), n); \\ Michel Marcus, Feb 19 2022
A384060
a(n) = [x^n] Product_{k=0..n} 1/(1 - k*x)^4.
Original entry on oeis.org
1, 4, 82, 3024, 162154, 11438280, 1001454024, 104777127616, 12755141675754, 1771354690734420, 276386332002204450, 47870892086756660064, 9113932961179205496744, 1891845220489637114281216, 425240943851497448491619600, 102899751348092720847554016000
Offset: 0
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Table[SeriesCoefficient[Product[1/(1-k*x)^4, {k, 1, n}], {x, 0, n}], {n, 0, 15}]
A384092
a(n) = [x^n] Product_{k=1..n} 1/(1 - k^2*x)^n.
Original entry on oeis.org
1, 1, 67, 19316, 14842986, 23959995900, 70300141076691, 340026368533209120, 2526875675012579004324, 27358621384723375076245950, 414013875603209906596527455633, 8469874364125222067804767445806552, 227937197746419681734617268030982470980, 7887251806534473871432104574423885714752540
Offset: 0
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Table[SeriesCoefficient[Product[1/(1-k^2*x)^n, {k, 0, n}], {x, 0, n}], {n, 0, 15}]
Showing 1-4 of 4 results.
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