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
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
A337155
a(n) = 5^n * (n!)^2 * Sum_{k=0..n} 1 / ((-5)^k * (k!)^2).
Original entry on oeis.org
1, 4, 81, 3644, 291521, 36440124, 6559222321, 1607009468644, 514243029966081, 208268427136262804, 104134213568131402001, 63001199208719498210604, 45360863430278038711634881, 38329929598584942711331474444, 37563331006613243857104844955121, 42258747382439899339242950574511124
Offset: 0
-
Table[5^n n!^2 Sum[1/((-5)^k k!^2), {k, 0, n}], {n, 0, 15}]
nmax = 15; CoefficientList[Series[BesselJ[0, 2 Sqrt[x]]/(1 - 5 x), {x, 0, nmax}], x] Range[0, nmax]!^2
-
a(n) = 5^n * (n!)^2 * sum(k=0, n, 1 / ((-5)^k * (k!)^2)); \\ Michel Marcus, Jan 28 2021
Showing 1-4 of 4 results.