A160906 Row sums of A159841.

1, 5, 29, 176, 1093, 6885, 43796, 280600, 1807781, 11698223, 75973189, 494889092, 3231947596, 21153123932, 138712176296, 911137377456, 5993760282021, 39481335979779, 260377117268087, 1719026098532296, 11360252318843933

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..n} A159841(n,k).

Conjecture: a(2n+1) = A075273(3n).

a(n) = C(3*n+1,n)*Hyper2F1([1,-n],[2*n+2],-1). - Peter Luschny, May 19 2015

Conjecture: 2*n*(2*n-1)*(5*n-4)*a(n) +(-295*n^3+451*n^2-130*n-24)*a(n-1) +24*(5*n+1)*(3*n-4)*(3*n-2)*a(n-2) = 0. - R. J. Mathar, Jul 20 2016

a(n) = [x^n] 1/((1 - 2*x)*(1 - x)^(2*n+1)). - Ilya Gutkovskiy, Oct 25 2017

a(n) ~ 3^(3*n + 3/2) / (sqrt(Pi*n) * 2^(2*n + 1)). - Vaclav Kotesovec, Oct 25 2017

Maple

A160906 := proc(n) add( A159841(n, k), k=0..n) ; end:
seq(A160906(n), n=0..20) ;

Mathematica

Table[Sum[Binomial[3*n+1, 2*n+k+1], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 25 2017 *)

Prog

(Sage)
a = lambda n: binomial(3*n+1, n)*hypergeometric([1, -n], [2*n+2], -1)
[simplify(a(n)) for n in range(21)] # Peter Luschny, May 19 2015
(PARI) a(n) = sum(k=0, n, binomial(3*n+1, 2*n+k+1)); \\ Michel Marcus, Oct 31 2017

Crossrefs

Cf. A075273, A159841.

Sequence in context: A083066 A327557 A163611 * A163073 A190802 A139174

Adjacent sequences: A160903 A160904 A160905 * A160907 A160908 A160909

Keyword

nonn,easy

Author

R. J. Mathar, May 29 2009

Status

approved