OFFSET
0,1
COMMENTS
Let H be the n X n Hilbert matrix H(i,j) = 1/(i+j-1) for 1 <= i,j <= n. Let B be the inverse matrix of H. The sum of the elements in row n-2 of B equals a(n-3). - T. D. Noe, May 01 2011
REFERENCES
J. Ser, Les Calculs Formels des Séries de Factorielles. Gauthier-Villars, Paris, 1933, p. 93.
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
G. C. Greubel, Table of n, a(n) for n = 0..1000
J. Ser, Les Calculs Formels des Séries de Factorielles, Gauthier-Villars, Paris, 1933 [Local copy].
J. Ser, Les Calculs Formels des Séries de Factorielles (Annotated scans of some selected pages)
FORMULA
From Alois P. Heinz, May 02 2011: (Start)
a(n) = 3*binomial(2*n+3,n)*binomial(n+3,n).
G.f.: 3*(1 + 6*x)/(1-4*x)^(7/2). (End)
a(n) = binomial(2*n+3,n)*(n^3 + 6*n^2 + 11*n+6)/2. - Charles R Greathouse IV, May 02 2011
a(n) = 3*A007744(n). - R. J. Mathar, Jan 21 2020
MATHEMATICA
Table[Total[Inverse[HilbertMatrix[n]][[n - 2]]], {n, 3, 25}] (* T. D. Noe, May 02 2011 *)
PROG
(Magma) [3*Binomial(2*n+3, n)*Binomial(n+3, 3): n in [0..30]]; // G. C. Greubel, Mar 21 2022
(Sage) [3*binomial(2*n+3, 3)*binomial(2*n, n) for n in (0..30)] # G. C. Greubel, Mar 21 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Extended by T. D. Noe, May 01 2011
STATUS
approved