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
A336807
a(n) = (n!)^2 * Sum_{k=0..n} 4^(n-k) / (k!)^2.
Original entry on oeis.org
1, 5, 81, 2917, 186689, 18668901, 2688321745, 526911062021, 134889231877377, 43704111128270149, 17481644451308059601, 8461115914433100846885, 4873602766713466087805761, 3294555470298303075356694437, 2582931488713869611079648438609, 2324638339842482649971683594748101
Offset: 0
-
Table[n!^2 Sum[4^(n - k)/k!^2, {k, 0, n}], {n, 0, 15}]
nmax = 15; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(1 - 4 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
A337152
a(n) = 2^n * (n!)^2 * Sum_{k=0..n} 1 / ((-2)^k * (k!)^2).
Original entry on oeis.org
1, 1, 9, 161, 5153, 257649, 18550729, 1817971441, 232700344449, 37697455800737, 7539491160147401, 1824556860755671041, 525472375897633259809, 177609663053400041815441, 69622987916932816391652873, 31330344562619767376243792849, 16041136416061320896636821938689
Offset: 0
-
Table[2^n n!^2 Sum[1/((-2)^k k!^2), {k, 0, n}], {n, 0, 16}]
nmax = 16; CoefficientList[Series[BesselJ[0, 2 Sqrt[x]]/(1 - 2 x), {x, 0, nmax}], x] Range[0, nmax]!^2
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a(n) = 2^n * (n!)^2 * sum(k=0, n, 1 / ((-2)^k * (k!)^2)); \\ Michel Marcus, Jan 28 2021
Showing 1-4 of 4 results.