A239453 Convolution of the generalized Catalan numbers A057977 with themselves.

1, 2, 3, 8, 11, 30, 43, 112, 172, 420, 694, 1584, 2809, 6006, 11379, 22880, 46088, 87516, 186562, 335920, 754646, 1293292, 3050238, 4992288, 12319816, 19315400, 49725004, 74884320, 200571541, 290845350, 808559299, 1131445440, 3257808976, 4407922860, 13119940234

Offset

0,2

Links

Table of n, a(n) for n=0..34.

Formula

D-finite with recurrence -(n+4)*(137*n-1035)*a(n) +(383*n^2-1622*n-5421)*a(n-1) +4*(274*n^2-1385*n-3534)*a(n-2) +4*(-766*n^2+4393*n+555)*a(n-3) +16*(-137*n^2+898*n-606)*a(n-4) +16*(n-3)*(383*n-1622)*a(n-5)=0. - R. J. Mathar, Feb 03 2025

Prog

(Sage)
def A239453_list(n):
    r = sqrt(1-4*x^2)
    g = lambda x: (1-r)*(r+x)/(2*x^2*r)
    s = taylor(g(x), x, 0, n+1)
    f = [s.coefficient(x, j) for j in (0..n+1)]
    return [add(f[k]*f[j-k] for k in (0..j)) for j in (0..n)]
A239453_list(36)

Crossrefs

Cf. A162551.

Sequence in context: A285113 A335632 A048788 * A143914 A041123 A042045

Adjacent sequences: A239450 A239451 A239452 * A239454 A239455 A239456

Keyword

nonn

Author

Peter Luschny, Mar 19 2014

Status

approved