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A160906 Row sums of A159841. 1
1, 5, 29, 176, 1093, 6885, 43796, 280600, 1807781, 11698223, 75973189, 494889092, 3231947596, 21153123932, 138712176296, 911137377456, 5993760282021, 39481335979779, 260377117268087, 1719026098532296, 11360252318843933 (list; graph; refs; listen; history; text; internal format)
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: A272802 A083066 A163611 * A163073 A190802 A139174

Adjacent sequences:  A160903 A160904 A160905 * A160907 A160908 A160909

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, May 29 2009

STATUS

approved

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Last modified April 27 01:03 EDT 2018. Contains 303149 sequences. (Running on oeis4.)