A371753 a(n) = Sum_{k=0..floor(n/2)} binomial(5*n-2*k-1,n-2*k).

1, 4, 37, 376, 4013, 44064, 492871, 5585080, 63901421, 736575316, 8540549322, 99503540008, 1163910870767, 13660217796736, 160782910480936, 1897131524755896, 22433316399634669, 265775992115557076, 3154067508987675679, 37487016824453703920, 446148092364247390618

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = [x^n] 1/((1-x^2) * (1-x)^(4*n)).

a(n) ~ 5^(5*n + 3/2) / (3 * sqrt(Pi*n) * 2^(8*n + 5/2)). - Vaclav Kotesovec, Apr 05 2024

Conjecture D-finite with recurrence +1024*n*(796184150374453*n -1374782084855770) *(4*n-3)*(2*n-1)*(4*n-1)*a(n) +64*(-4720591427354845074*n^5 +16046598674673412696*n^4 -14164434258362644374*n^3 -6132680339747354209*n^2 +16406971563067867560*n -7312237120275595200)*a(n-1) +40*(-4968388566264801507*n^5 +51044954667717039608*n^4 -218029351288077225930*n^3 +471970442274586326109*n^2 -511707487331990011785*n +221366817798624198360)*a(n-2) -25*(5*n-11) *(719005061479699*n -1438086256867727)*(5*n-9) *(5*n-13)*(5*n-12)*a(n-3)=0. - R. J. Mathar, Sep 27 2024

Maple

A371753 := proc(n)
    add( binomial(5*n-2*k-1, n-2*k), k=0..floor(n/2)) ;
end proc:
seq(A371753(n), n=0..50) ; # R. J. Mathar, Sep 27 2024

Prog

(PARI) a(n) = sum(k=0, n\2, binomial(5*n-2*k-1, n-2*k));

Crossrefs

Cf. A026641, A147855, A183160.

Sequence in context: A199690 A133462 A123762 * A326014 A220914 A070768

Adjacent sequences: A371750 A371751 A371752 * A371754 A371755 A371756

Keyword

nonn

Author

Seiichi Manyama, Apr 05 2024

Status

approved