A041001 Convolution of A000108(n+1), n >= 0, (Catalan numbers) with A038845 (3-fold convolution of powers of 4).

1, 14, 125, 906, 5810, 34364, 191901, 1026610, 5312230, 26767940, 131990066, 639210404, 3048892740, 14354652152, 66828135005, 308078809794, 1408022619806, 6385966846580, 28765327498278, 128777533131500

Offset

0,2

Comments

Also convolution of A038836 with A000984 (central binomial coefficients); also convolution of A001791(n+1), n >= 0, with A002802; also convolution of A008549(n+1), n >= 0, with A002697; also convolution of A029760 with A002457; also convolution of A038806(n+1), n >= 0, with A000302 (powers of 4).

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = (n+3)*(3*(n+6)*2^(2*n+3)-(n+4)*binomial(2*n+7, n+3))/12; G.f. (c(x)^2)/(1-4*x)^3, where c(x) = g.f. for Catalan numbers.

Crossrefs

Sequence in context: A155637 A126535 A222647 * A025211 A026870 A090296

Adjacent sequences: A040998 A040999 A041000 * A041002 A041003 A041004

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved