A354941
a(n) = Sum_{k=0..n} binomial(n,k)^3 * k! * (-2)^(n-k).
Original entry on oeis.org
1, -1, -10, -2, 488, 4088, -9968, -730480, -9751936, -11540096, 2480655104, 62522038016, 680469314560, -8292439149568, -606011029669888, -15765339965278208, -183530875864317952, 4164677242501038080, 318357069130977181696, 10359690304436314505216, 176911847384965046337536
Offset: 0
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Table[Sum[Binomial[n, k]^3 k! (-2)^(n - k), {k, 0, n}], {n, 0, 20}]
nmax = 20; CoefficientList[Series[BesselI[0, 2 Sqrt[x]] Sum[(-2)^k x^k/k!^3, {k, 0, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^3
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a(n) = sum(k=0, n, binomial(n,k)^3 * k! * (-2)^(n-k)); \\ Michel Marcus, Jun 12 2022
A354942
a(n) = Sum_{k=0..n} binomial(n,k)^3 * k! * (-3)^(n-k).
Original entry on oeis.org
1, -2, -13, 60, 1113, 1002, -149049, -1932696, 7188705, 676972566, 10821753819, -32865363468, -5892948042327, -144308265498270, -748826955982593, 74472859430936928, 3199088479682040129, 57854159449349840046, -654712764990637945725, -87482030500940669619156
Offset: 0
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Table[Sum[Binomial[n, k]^3 k! (-3)^(n - k), {k, 0, n}], {n, 0, 19}]
nmax = 19; CoefficientList[Series[BesselI[0, 2 Sqrt[x]] Sum[(-3)^k x^k/k!^3, {k, 0, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^3
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a(n) = sum(k=0, n, binomial(n,k)^3 * k! * (-3)^(n-k)); \\ Michel Marcus, Jun 12 2022
A354944
a(n) = Sum_{k=0..n} binomial(n,k)^3 * k! * (-n)^(n-k).
Original entry on oeis.org
1, 0, -10, 60, 1560, -39880, -491760, 45672060, -155935360, -77656158000, 2116774828800, 166585352850620, -11925674437248000, -330617542587341880, 69148933431781898240, -543549949643024194500, -434534462104188331130880, 21521903478880966780355360
Offset: 0
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Unprotect[Power]; 0^0 = 1; Table[Sum[Binomial[n, k]^3 k! (-n)^(n - k), {k, 0, n}], {n, 0, 17}]
Unprotect[Power]; 0^0 = 1; Table[n!^3 SeriesCoefficient[BesselI[0, 2 Sqrt[x]] Sum[(-n)^k x^k/k!^3, {k, 0, n}], {x, 0, n}], {n, 0, 17}]
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a(n) = sum(k=0, n, binomial(n,k)^3 * k! * (-n)^(n-k)); \\ Michel Marcus, Jun 12 2022
Showing 1-3 of 3 results.