A000386 a(n) = A058057(n,n-3). (Formerly M4137 N1715)

0, 0, 0, 1, 6, 20, 134, 915, 7324, 65784, 657180, 7223637, 86637650, 1125842556, 15757002706, 236298742375, 3780061394232, 64251145312880, 1156374220457784, 21968796934412649, 439337048505773790, 9225384943965382564, 202945418255342821470

Offset

0,5

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 = 0..450

Formula

a(n) = -Sum_{k=3..n} (-1)^k * (n-k)! * binomial(k,3) * binomial(2*n-k,k). - Seiichi Manyama, Jun 21 2026

Mathematica

max = 22; 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_] := If[n<3, 0, t[[n+1, n-2]]]; Table[ a[n], {n, 0, max}] (* Jean-François Alcover, Feb 08 2016, after Vladeta Jovovic in A058057 *)

Prog

(PARI) a(n) = -sum(k=3, n, (-1)^k*(n-k)!*binomial(k, 3)*binomial(2*n-k, k)); \\ Seiichi Manyama, Jun 21 2026

Crossrefs

A diagonal of A058057.

Sequence in context: A074013 A333896 A114959 * A000387 A145221 A332391

Adjacent sequences: A000383 A000384 A000385 * A000387 A000388 A000389

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Name changed by Seiichi Manyama, Jun 21 2026

Status

approved