A042940 Convolution of Catalan numbers A000108(n+1), n >= 0, with A038846.

1, 18, 197, 1694, 12586, 84708, 530733, 3149542, 17910398, 98409532, 525628194, 2741723180, 14015785460, 70417793992, 348499310973, 1702076053686, 8216326834550, 39251274184780, 185770424237398, 871859230081092

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Also convolution of A018218(n+1), n >= 0, with itself; also convolution of A041001 with A000302 (powers of 4); also convolution of A041005 with A000984 (central binomial coefficients).

Formula

a(n) = binomial(n+4, 2)*((n+8)*A001700(2)*4^(n+1)-A002457(n+4)/2)/A002457(2), A001700(2)= 10, A002457(2)=30; G.f. (c(x)^2)/(1-4*x)^4, where c(x) = g.f. for Catalan numbers.