A041005 Convolution of Catalan numbers A000108(n+1), n >= 0, with A020918.

1, 16, 159, 1260, 8722, 55152, 326811, 1844084, 10015566, 52754624, 270976342, 1362986520, 6734927460, 32775704608, 157408497171, 747269225028, 3511471892470, 16351481223840, 75525932249922, 346305571781224

Offset

0,2

Comments

Also convolution of A001791(n+1), n >= 0, with A038845; also convolution of A008549(n+1), n >= 0, with A002802; also convolution of A029760 with A002697; also convolution of A038806(n+1), n >= 0, with A002457; also convolution of A038836 with A000302 (powers of 4); also convolution of A041001 with A000984 (central binomial coefficients).

Links

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

Formula

a(n)=binomial(n+7, 3)*binomial(2*(n+4), n+2)/20 - (n+4)*(n+3)*4^(n+1); G.f. (c(x)^2)/(1-4*x)^(7/2), where c(x) = g.f. for Catalan numbers.

Crossrefs

Sequence in context: A036973 A101931 A220630 * A180798 A144453 A121036

Adjacent sequences: A041002 A041003 A041004 * A041006 A041007 A041008

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved