A034749 Dirichlet convolution of Fibonacci numbers with Catalan numbers.

1, 2, 4, 9, 19, 54, 145, 458, 1468, 4936, 16885, 58996, 208245, 743422, 2675088, 9696297, 35359267, 129648938, 477642881, 1767274939, 6564131656, 24466301616, 91482592297, 343059720014, 1289904222419, 4861946731090