cp's OEIS Frontend

a(n) = Sum_{k=0..n-1} C(n-k,k)/(n-k) * C(6*k,n-k-1) for n>0 with a(0)=1. - Paul D. Hanna, Jun 16 2009

Recurrence: 5*(n-1)*n*(5*n - 26)*(5*n - 21)*(5*n - 19)*(5*n - 16)*(5*n - 14)*(5*n - 12)*(5*n - 11)*(5*n - 9)*(5*n - 7)*(5*n - 6)*(5*n - 4)*(5*n - 2)*(5*n + 2)*a(n) = + 576*(n-1)^2*(3*n - 5)*(3*n - 4)*(3*n - 2)*(3*n - 1)*(5*n - 26)*(5*n - 21)*(5*n - 19)*(5*n - 16)*(5*n - 14)*(5*n - 12)*(5*n - 11)*(5*n - 9)*(5*n - 7)*a(n-2) + 288*(3*n - 5)*(3*n - 4)*(5*n - 26)*(5*n - 21)*(5*n - 19)*(5*n - 16)*(5*n - 14)*(5*n - 12)*(11250*n^7 - 111375*n^6 + 440175*n^5 - 888545*n^4 + 975241*n^3 - 574177*n^2 + 165869*n - 18018)*a(n-3) + 144*(5*n - 26)*(5*n - 21)*(5*n - 19)*(5*n - 6)*(10125000*n^11 - 218700000*n^10 + 2075585625*n^9 - 11378954250*n^8 + 39836289925*n^7 - 92894908470*n^6 + 145953551806*n^5 - 152681445300*n^4 + 102505633480*n^3 - 41086190160*n^2 + 8557182144*n - 670602240)*a(n-4) + 72*(5*n - 26)*(5*n - 11)*(5*n - 6)*(5*n - 4)*(20250000*n^11 - 569025000*n^10 + 7025658750*n^9 - 50083579125*n^8 + 227686012400*n^7 - 687547140050*n^6 + 1391232445598*n^5 - 1854143517725*n^4 + 1550931293540*n^3 - 737424345140*n^2 + 162058858752*n - 10360465920)*a(n-5) + 144*(5*n - 16)*(5*n - 11)*(5*n - 9)*(5*n - 6)*(5*n - 4)*(5*n - 2)*(202500*n^9 - 5953500*n^8 + 74924775*n^7 - 526434885*n^6 + 2255339082*n^5 - 6025054075*n^4 + 9796892735*n^3 - 8893818500*n^2 + 3545754268*n - 142331280)*a(n-6) + 72*n*(2*n - 9)*(3*n - 17)*(3*n - 10)*(5*n - 21)*(5*n - 16)*(5*n - 14)*(5*n - 11)*(5*n - 9)*(5*n - 7)*(5*n - 6)*(5*n - 4)*(5*n - 2)*(6*n - 41)*(6*n - 13)*a(n-7). - Vaclav Kotesovec, Nov 18 2017

a(n) ~ sqrt((1 + 2*r*s^6)/(15*Pi)) / (2*s^2 * n^(3/2) * r^(n + 1/2)), where r = 0.1734895129039028676461340698295316044509963479582... and s = 1.408187415484683441175360883795437925341195617549... are roots of the system of equations 1 + r + r^2*s^6 = s, 6*r^2*s^5 = 1. - Vaclav Kotesovec, Nov 18 2017

G.f.: A(x) = 1 + x*B(x)^5 where B(x) is the g.f. of A137960.

a(n) = Sum_{k=0..n-1} C(5*(n-k),k)/(n-k) * C(2*k,n-k-1) for n>0 with a(0)=1. - Paul D. Hanna, Jun 16 2009

a(n) ~ sqrt(5*s*(1-s)*(2-3*s) / ((36*s - 20)*Pi)) / (n^(3/2) * r^n), where r = 0.1354712934479194768810666044866029126617104117352... and s = 1.618016818966151244027202981456410137451426090894... are real roots of the system of equations s = 1 + r*(1 + r*s^2)^5, 10 * r^2 * s * (1 + r*s^2)^4 = 1. - Vaclav Kotesovec, Nov 22 2017

G.f.: A(x) = 1 + x*B(x)^5 where B(x) is the g.f. of A137962.

a(n) = Sum_{k=0..n-1} C(5*(n-k),k)/(n-k) * C(3*k,n-k-1) for n>0 with a(0)=1. - Paul D. Hanna, Jun 16 2009

a(n) ~ sqrt(5*s*(1-s)*(3-4*s) / ((84*s - 60)*Pi)) / (n^(3/2) * r^n), where r = 0.1085884782751570249717333800652227343328635496829... and s = 1.404764002126311415321709718173984955120001713401... are real roots of the system of equations s = 1 + r*(1 + r*s^3)^5, 15 * r^2 * s^2 * (1 + r*s^3)^4 = 1. - Vaclav Kotesovec, Nov 22 2017

G.f.: A(x) = 1 + x*B(x)^4 where B(x) is the g.f. of A137965.

a(n) = Sum_{k=0..n-1} C(4*(n-k),k)/(n-k) * C(5*k,n-k-1) for n>0 with a(0)=1. - Paul D. Hanna, Jun 16 2009

a(n) ~ sqrt(4*s*(1-s)*(5-6*s) / ((190*s - 160)*Pi)) / (n^(3/2) * r^n), where r = 0.0927175295193852172913829423030505161354091369581... and s = 1.270497495855793662015513509713357933752729700697... are real roots of the system of equations s = 1 + r*(1 + r*s^5)^4, 20 * r^2 * s^4 * (1 + r*s^5)^3 = 1. - Vaclav Kotesovec, Nov 22 2017

G.f.: A(x) = 1 + x*B(x)^5 where B(x) is the g.f. of A137974.

a(n) = Sum_{k=0..n-1} C(5*(n-k),k)/(n-k) * C(6*k,n-k-1) for n>0 with a(0)=1. - Paul D. Hanna, Jun 16 2009

a(n) ~ sqrt(5*s*(1-s)*(6-7*s) / ((348*s - 300)*Pi)) / (n^(3/2) * r^n), where r = 0.0739607593319208338998816978154858830062403258604... and s = 1.212436147090690045831533523759068212147683922018... are real roots of the system of equations s = 1 + r*(1 + r*s^6)^5, 30 * r^2 * s^5 * (1 + r*s^6)^4 = 1. - Vaclav Kotesovec, Nov 22 2017