A054443 Third convolution of A001405 (central binomial numbers).

1, 4, 14, 40, 109, 276, 682, 1624, 3810, 8744, 19868, 44496, 98941, 217780, 476786, 1036024, 2241814, 4823160, 10342180, 22076080, 46994386, 99673224, 210923364, 445000560, 937051684, 1968204496, 4127285688, 8636324768, 18045851165, 37638105588, 78404375362

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(2*k) = (2*k+7)*4^(k+1)-binomial(2*(k+2), k+2)*(4*k+9)/2, a(2*k+1) = (k+4)*4^(k+2)-(k+3)*binomial(2*(k+3), k+3), k >= 0.

a(n) = A054336(n+3, 3) (fourth column of convolution triangle). G.f.: (1/(1-x-x^2*c(x^2)))^4, with c(x) the g.f. for the Catalan numbers A000108.

G.f.: (c(x/(2x-1))/(1-2x))^4. - Michael Somos, Jul 31 2005

Prog

(PARI) {a(n)=local(k); if(n<0, 0, k=n\2; if(n%2, (k+4)*4^(k+2)-(k+3)*binomial(2*(k+3), k+3), (2*k+7)*4^(k+1)-binomial(2*(k+2), k+2)*(4*k+9)/2 ))}

Crossrefs

Cf. A000108, A001405, A054336, A054442.

Sequence in context: A160527 A023003 A001872 * A281766 A072674 A202900

Adjacent sequences: A054440 A054441 A054442 * A054444 A054445 A054446

Keyword

easy,nonn

Author

Wolfdieter Lang, Mar 27 2000

Status

approved