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
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
A337153
a(n) = 3^n * (n!)^2 * Sum_{k=0..n} 1 / ((-3)^k * (k!)^2).
Original entry on oeis.org
1, 2, 25, 674, 32353, 2426474, 262059193, 38522701370, 7396358663041, 1797315155118962, 539194546535688601, 195727620392454962162, 84554332009540543653985, 42869046328837055632570394, 25206999241356188711951391673, 17014724487915427380567189379274, 13067308406719048228275601443282433
Offset: 0
-
Table[3^n n!^2 Sum[1/((-3)^k k!^2), {k, 0, n}], {n, 0, 16}]
nmax = 16; CoefficientList[Series[BesselJ[0, 2 Sqrt[x]]/(1 - 3 x), {x, 0, nmax}], x] Range[0, nmax]!^2
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a(n) = 3^n * (n!)^2 * sum(k=0, n, 1 / ((-3)^k * (k!)^2)); \\ Michel Marcus, Jan 28 2021
Showing 1-4 of 4 results.