A336804
a(n) = (n!)^2 * Sum_{k=0..n} 2^(n-k) / (k!)^2.
Original entry on oeis.org
1, 3, 25, 451, 14433, 721651, 51958873, 5091969555, 651772103041, 105587080692643, 21117416138528601, 5110414705523921443, 1471799435190889375585, 497468209094520608947731, 195007537965052078707510553, 87753392084273435418379748851, 44929736747147998934210431411713
Offset: 0
-
Table[n!^2 Sum[2^(n - k)/k!^2, {k, 0, n}], {n, 0, 16}]
nmax = 16; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(1 - 2 x), {x, 0, nmax}], x] Range[0, nmax]!^2
A336805
a(n) = (n!)^2 * Sum_{k=0..n} 3^(n-k) / (k!)^2.
Original entry on oeis.org
1, 4, 49, 1324, 63553, 4766476, 514779409, 75672573124, 14529134039809, 3530579571673588, 1059173871502076401, 384480115355253733564, 166095409833469612899649, 84210372785569093740122044, 49515699197914627119191761873, 33423096958592373305454439264276, 25668938464198942698589009354963969
Offset: 0
-
Table[n!^2 Sum[3^(n - k)/k!^2, {k, 0, n}], {n, 0, 16}]
nmax = 16; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(1 - 3 x), {x, 0, nmax}], x] Range[0, nmax]!^2
A336808
a(n) = (n!)^2 * Sum_{k=0..n} 5^(n-k) / (k!)^2.
Original entry on oeis.org
1, 6, 121, 5446, 435681, 54460126, 9802822681, 2401691556846, 768541298190721, 311259225767242006, 155629612883621003001, 94155915794590706815606, 67792259372105308907236321, 57284459169428986026614691246, 56138769986040406306082397421081, 63156116234295457094342697098716126
Offset: 0
-
Table[n!^2 Sum[5^(n - k)/k!^2, {k, 0, n}], {n, 0, 15}]
nmax = 15; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(1 - 5 x), {x, 0, nmax}], x] Range[0, nmax]!^2
A337154
a(n) = 4^n * (n!)^2 * Sum_{k=0..n} 1 / ((-4)^k * (k!)^2).
Original entry on oeis.org
1, 3, 49, 1763, 112833, 11283299, 1624795057, 318459831171, 81525716779777, 26414332236647747, 10565732894659098801, 5113814721015003819683, 2945557279304642200137409, 1991196720809938127292888483, 1561098229114991491797624570673, 1404988406203492342617862113605699
Offset: 0
-
Table[4^n n!^2 Sum[1/((-4)^k k!^2), {k, 0, n}], {n, 0, 15}]
nmax = 15; CoefficientList[Series[BesselJ[0, 2 Sqrt[x]]/(1 - 4 x), {x, 0, nmax}], x] Range[0, nmax]!^2
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a(n) = 4^n * (n!)^2 * sum(k=0, n, 1 / ((-4)^k * (k!)^2)); \\ Michel Marcus, Jan 28 2021
Showing 1-4 of 4 results.