A000450 a(n) = A058057(n,n-4). (Formerly M4709 N2012)

1, 10, 50, 385, 3130, 28764, 291900, 3249210, 39367395, 515874470, 7270929806, 109691447395, 1763782644020, 30114243100760, 544123405603800, 10373304279494964, 208092476689208805, 4381794437494059810, 96635643877147885450, 2227562535558247510885

Offset

4,2

References

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 198.

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

Seiichi Manyama, Table of n, a(n) for n = 4..450

R. C. Read, Letter to N. J. A. Sloane, Oct. 29, 1976

Formula

a(n) = Sum_{k=4..n} (-1)^k * (n-k)! * binomial(k,4) * binomial(2*n-k,k). - Seiichi Manyama, Jun 21 2026

Mathematica

max = 23; f[x_, y_] := Sum[n!*((x*y)^n/(1 + x*(y-1))^(2*n+1)), {n, 0, max} ]; t = MapIndexed[Take[#1, #2[[1]]]&, CoefficientList[Series[f[x, y], {x, 0, max}, {y, 0, max}], {x, y}]]; a[n_] := t[[n+1, n-3]]; Table[a[n], {n, 4, max}] (* Jean-François Alcover, Feb 08 2016, after Vladeta Jovovic in A058057 *)

Prog

(PARI) a(n) = sum(k=4, n, (-1)^k*(n-k)!*binomial(k, 4)*binomial(2*n-k, k)); \\ Seiichi Manyama, Jun 21 2026

Crossrefs

A diagonal of A058057.

Sequence in context: A154410 A395026 A060156 * A124872 A240534 A223161

Adjacent sequences: A000447 A000448 A000449 * A000451 A000452 A000453

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Extensions

Name changed by Seiichi Manyama, Jun 21 2026

Status

approved