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A133602 The matrix-vector product A133080 * A000108.

%I A133602 #15 Jun 06 2020 15:32:32
%S A133602 1,2,2,7,14,56,132,561,1430,6292,16796,75582,208012,950912,2674440,
%T A133602 12369285,35357670,165002460,477638700,2244901890,6564120420,
%U A133602 31030387440,91482563640,434542177290,1289904147324,6151850548776
%N A133602 The matrix-vector product A133080 * A000108.
%C A133602 A133603 is a companion sequence.
%F A133602 A133080 * A000108, where A133080 = an infinite lower triangular matrix and A000108 = the Catalan sequence as a vector.
%F A133602 a(2n) = A048990(n).
%F A133602 a(2n+1) = A005807(2n).
%F A133602 Conjecture: n*(n-1)*(n-3)*(3*n-4)*a(n) -8*(n-1)*(2*n-5)*a(n-1) -4*(n-2)*(3*n-1)*(2*n-5)*(2*n-7)*a(n-2)=0. - _R. J. Mathar_, Jun 20 2015
%e A133602 a(4) = C(4) = 14.
%e A133602 a(5) = 56 = C(5) + C(4) = 42 + 14.
%o A133602 (Python)
%o A133602 from sympy import catalan
%o A133602 def a005807(n): return catalan(n) + catalan(n + 1)
%o A133602 def a048990(n): return catalan(2*n)
%o A133602 l=[1, 2]
%o A133602 for n in range(2, 31): l+=[a048990(n//2) if n%2==0 else a005807(n - 1)]
%o A133602 print(l) # _Indranil Ghosh_, Jul 15 2017
%Y A133602 Cf. A097806, A133080, A000108, A133603.
%K A133602 nonn,easy
%O A133602 0,2
%A A133602 _Gary W. Adamson_, Sep 18 2007