A038836 Convolution of Catalan numbers {1,2,5,14,...} with A002802 (5-fold convoluted central binomial coefficients).

1, 12, 95, 624, 3682, 20264, 106203, 536840, 2639230, 12692360, 59957846, 279081152, 1282981380, 5835994768, 26305678739, 117635236344, 522394992358, 2305593653960, 10120007354562, 44201842781536, 192208416186716

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Convolution of A038806(n+1), n >= 0, with A000984 (central binomial coefficients); also convolution of A029760 with A000302 (powers of 4).

Crossrefs

Cf. A000108, A002802, A000302, A000984, A029760, A038806.

Formula

a(n) = binomial(n+5, 2)*binomial(2*(n+3), n+2)/6 - (n+3)*2^(2*n+3); G.f. c(x)^2/(1-4*x)^(5/2), where c(x) = g.f. for Catalan numbers A000108;