A218692 Sum_{k=0..n} C(n,k)^6*C(n+k,k)^3.

1, 9, 1945, 783657, 333935001, 216152253009, 148273286805001, 112444816742316585, 93273051852487532953, 80885382627785790555009, 73726153308964013326434945, 69714999360408389332640853105, 67921574835559806028030517001225, 67965584346796032477336615843457665

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

V. Kotesovec, Asymptotic of generalized Apery sequences with powers of binomial coefficients, Nov 04 2012

Formula

a(n) ~ ((1+sqrt(5))/2)^(3*(5*n+4)-3/2)/(5^(1/4)*(2*Pi*n)^4*sqrt(3))

Generally, Sum_{k=0..n} C(n,k)^(2*q)*C(n+k,k)^q is asymptotic to ((1+sqrt(5))/2)^(q*(5*n+4)-3/2)/(5^(1/4)*sqrt(q*(2*Pi*n)^(3*q-1))) * (1-(25*q^2+96*q-61)/(120*q*n)-(13*q^2-36*q+17)*sqrt(5)/(60*q*n)).

Mathematica

Table[Sum[Binomial[n, k]^6*Binomial[n+k, k]^3, {k, 0, n}], {n, 0, 20}]

Crossrefs

Cf. A005258, A218690.

Sequence in context: A194135 A114224 A201845 * A024125 A232684 A039917

Adjacent sequences: A218689 A218690 A218691 * A218693 A218694 A218695

Keyword

nonn

Author

Vaclav Kotesovec, Nov 04 2012

Status

approved