A007744 -id:A007744 - cp's OEIS frontend

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

N. J. A. Sloane

nonn

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

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).

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)

Cf. A002802, A007744, A020918.

A diagonal of A331431.

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

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

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

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

Extended by T. D. Noe, May 01 2011

A106440 a(n) = binomial(2n+4,n)*binomial(n+4,4).

Original entry on oeis.org

1, 30, 420, 4200, 34650, 252252, 1681680, 10501920, 62355150, 355655300, 1963217256, 10546208400, 55367594100, 285028443000, 1442592936000, 7193730107520, 35406640372950, 172255143129300, 829376615067000

Offset: 0

Paul Barry, May 02 2005

Fifth column of A104684.

Diagonal of the rational function 1 / (1 - x - y)^5. - Ilya Gutkovskiy, Apr 24 2025

Michael De Vlieger, Table of n, a(n) for n = 0..1642
Ömür Deveci and Anthony G. Shannon, Some aspects of Neyman triangles and Delannoy arrays, Mathematica Montisnigri (2021) Vol. L, 36-43.

Cf. A007744, A002544, A002457.

Cf. A002803, A020920.

Table[Binomial[2n+4,n]Binomial[n+4,4],{n,0,20}] (* Harvey P. Dale, May 03 2019 *)

G.f.: (1+12x+6x^2)/(1-4x)^(9/2).
D-finite with recurrence n^2*a(n) -2*(n+2)*(2*n+3)*a(n-1)=0. - R. J. Mathar, Feb 20 2015
G.f.: 2F1(5/2,3;1;4x). - R. J. Mathar, Aug 09 2015
a(n) = A020920(n)+12*A020920(n-1)+6*A020920(n-2). - R. J. Mathar, Aug 09 2015
a(n) = (n+1)*A002803(n). - R. J. Mathar, Aug 09 2015

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A002738 Coefficients for extrapolation.

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