A002738 Coefficients for extrapolation. (Formerly M3165 N1283)

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

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

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

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

Cf. A002802, A007744, A020918.

A diagonal of A331431.

Sequence in context: A195560 A229749 A283381 * A006432 A360577 A195550

Adjacent sequences: A002735 A002736 A002737 * A002739 A002740 A002741

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Extended by T. D. Noe, May 01 2011

Status

approved