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A277395 a(n) = Sum_{k=0..n} binomial(n+1,k+1)*A001003(k). 0
1, 3, 9, 33, 145, 713, 3745, 20513, 115713, 667329, 3916033, 23305857, 140327681, 853262465, 5231925761, 32313686529, 200843829249, 1255308123137, 7884792852481, 49745076576257, 315091155558401, 2003009460686849, 12774610185633793 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

FORMULA

G.f.: (1-sqrt(8*x^2-8*x+1))/(4*(1-x)^2*x).

Conjecture: (n+1)*a(n) +2*(-5*n+1)*a(n-1) +(25*n-23)*a(n-2) +12*(-2*n+3)*a(n-3)

+8*(n-2)*a(n-4)=0. - R. J. Mathar, Mar 12 2017

PROG

(Maxima)

g(k):=1/(k+1)*sum((-1)^j*2^(k-j)*binomial(k+1, j)*binomial(2*k-j, k), j, 0, k);

makelist(sum(binomial(n+1, k+1)*g(k), k, 0, n), n, 0, 23);

CROSSREFS

Cf. A001003.

Sequence in context: A193110 A001930 A049425 * A012584 A101899 A180632

Adjacent sequences:  A277392 A277393 A277394 * A277396 A277397 A277398

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Oct 12 2016

STATUS

approved

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Last modified February 22 05:58 EST 2018. Contains 299430 sequences. (Running on oeis4.)