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A054443 Third convolution of A001405 (central binomial numbers). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)