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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
OFFSET
0,2
LINKS
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
Sequence in context: A083066 A327557 A163611 * A163073 A190802 A139174
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, May 29 2009
STATUS
approved