OFFSET
1,2
REFERENCES
H. Bateman, Some problems in potential theory, Messenger Math., 52 (1922), 71-78.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n=1..100
H. Bateman, Some problems in potential theory, Messenger Math., 52 (1922), 71-78. [Annotated scanned copy]
John Riordan, Letter to N. J. A. Sloane, Sep 26 1980 with notes on the 1973 Handbook of Integer Sequences. Note that the sequences are identified by their N-numbers, not their A-numbers.
FORMULA
G.f.: x*(1-6*x+x^2)^(-3/2). [corrected by Vaclav Kotesovec, Oct 04 2012]
a(n) = Gegenbauer_C(n,3/2,3). - Paul Barry, Apr 20 2009
D-finite with recurrence: -n*a(n-2) + 3*(2*n-1)*a(n-1) + (1-n)*a(n) = 0. - Vaclav Kotesovec, Oct 04 2012
a(n) ~ (3+2*sqrt(2))^n*sqrt(n)/(4*sqrt(2*Pi)*sqrt(3*sqrt(2)-4)). - Vaclav Kotesovec, Oct 04 2012
a(n) = (n+1) * n * A001003(n)/2, n>0. - Vladimir Kruchinin, Mar 29 2013
a(n) = Sum_{i=1..n} i*binomial(n+i,i)*binomial(n,i)/2. - Gerry Martens, Apr 08 2018
MATHEMATICA
Table[SeriesCoefficient[x*(1-6x+x^2)^(-3/2), {x, 0, n}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 04 2012 *)
a[n_]:= Sum[(i Binomial[n+i+1, i] Binomial[n+1, i]), {i, 1, n+1}]/2
Table[a[n], {n, 0, 20}] (* Gerry Martens, Apr 08 2018 *)
PROG
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved