A247173 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A247173

Expansion of g.f. (-1)/(2*x^2+2*x) +(-2*x^3-3*x^2+1) / (sqrt(x^4+4*x^3-2*x^2-4*x+1)*(2*x^2+2*x)).

1, 1, 7, 25, 101, 397, 1583, 6337, 25513, 103161, 418727, 1705129, 6963165, 28504981, 116941727, 480667137, 1979039633, 8160609457, 33696358983, 139308985465, 576583448021, 2388853677981, 9906585874127, 41118073118785, 170799570803001, 710003165365417

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

FORMULA

a(n) = (n+1)*sum(k=0..n, (C(n-k-1,k)*sum(i=0..n-k, 2^i*C(k+1,n-k-i) *C(k+i,k)*(-1)^(n-k-i)))/(k+1)).

Conjecture D-finite with recurrence: -(n+1)*(3*n-4)*a(n) +(9*n^2-3*n-4)*a(n-1) +2*(9*n^2-21*n+8)*a(n-2) +2*(-3*n^2+n+8)*a(n-3) +(-15*n^2+53*n-12)*a(n-4) -(3*n-1)*(n-4)*a(n-5)=0. - R. J. Mathar, Jan 25 2020

a(n) ~ 5^(1/4) * phi^(3*n + 2) / (2^(3/2) * sqrt(Pi*n)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Nov 19 2021

PROG

(Maxima) a(n):=(n+1)*sum((binomial(n-k-1, k)*sum(2^i*binomial(k+1, n-k-i)*binomial(k+i, k)*(-1)^(n-k-i), i, 0, n-k))/(k+1), k, 0, n);

CROSSREFS

Sequence in context: A138729 A035509 A332942 * A141627 A289606 A102900

Adjacent sequences: A247170 A247171 A247172 * A247174 A247175 A247176

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Nov 22 2014

STATUS

approved