A002738 Coefficients for extrapolation.

3, 60, 630, 5040, 34650, 216216, 1261260, 7001280, 37413090, 193993800, 981608628, 4867480800, 23728968900, 114011377200, 540972351000, 2538963567360, 11802213457650, 54396360988200, 248812984520100, 1130341536324000, 5103492036502860, 22913637714910800

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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)

Crossrefs

Cf. A002802, A007744, A020918.

A diagonal of A331431.

Programs

Magma

[3*Binomial(2*n+3,n)*Binomial(n+3,3): n in [0..30]]; // G. C. Greubel, Mar 21 2022

Mathematica

Table[Total[Inverse[HilbertMatrix[n]][[n - 2]]], {n, 3, 25}] (* T. D. Noe, May 02 2011 *)

Sage

[3*binomial(2*n+3,3)*binomial(2*n,n) for n in (0..30)] # G. C. Greubel, Mar 21 2022

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

a(n) = (3/2)*( 5*A020918(n) - 3*A002802(n)). - G. C. Greubel, Mar 21 2022

Extensions

Extended by T. D. Noe, May 01 2011