A041001 -id:A041001 - cp's OEIS frontend

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

Wolfdieter Lang

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).

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.

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

Original entry on oeis.org

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

Offset: 0

Wolfdieter Lang

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).

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.

cp's OEIS Frontend

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

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