VOOZH about

URL: https://oeis.org/A007044

⇱ A007044 - OEIS

login
A007044
Left diagonal of partition triangle A047812.
4
0, 0, 1, 7, 20, 48, 100, 194, 352, 615, 1034, 1693, 2705, 4239, 6522, 9889, 14786, 21844, 31913, 46165, 66162, 94035, 132600, 185637, 258128, 356674, 489906, 669173, 909212, 1229217, 1653993, 2215597, 2955192, 3925659, 5194520, 6847963, 8995524, 11776227
OFFSET
1,4
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. K. Guy, Parker's permutation problem involves the Catalan numbers, Preprint, 1992. (Annotated scanned copy)
R. K. Guy, Parker's permutation problem involves the Catalan numbers, Amer. Math. Monthly 100 (1993), 287-289.
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(n<0
or t*i<n, 0, b(n, i-1, t)+b(n-i, min(i, n-i), t-1)))
end:
a:= n-> b(2*n+2, n$2):
seq(a(n), n=1..50); # Alois P. Heinz, May 31 2020
MATHEMATICA
b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, If[n < 0 || t i < n, 0, b[n, i - 1, t] + b[n - i, Min[i, n - i], t - 1]]];
a[n_] := b[2n+2, n, n];
Array[a, 50] (* Jean-François Alcover, Nov 23 2020, after Alois P. Heinz *)
PROG
(PARI) T(n, k) = polcoeff(prod(j=0, n-1, (1-q^(2*n-j))/(1-q^(j+1)) ), k*(n+1) );
for(n=1, 40, print1(T(n, 2), ", ")) \\ Petros Hadjicostas, May 31 2020
CROSSREFS
KEYWORD
nonn
EXTENSIONS
Name edited by Petros Hadjicostas, May 31 2020
STATUS
approved