A071735 Expansion of (1+x^3*C^3)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
1, 2, 5, 15, 47, 152, 504, 1705, 5863, 20436, 72046, 256462, 920550, 3328192, 12109270, 44305245, 162911415, 601700700, 2231255070, 8304089970, 31007435970, 116130446640, 436137803400, 1642112017338, 6197239974582, 23438771087272, 88826989017004, 337262603824860
Offset: 0
Keywords
Crossrefs
First differences of A000782.
Programs
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Maxima
a(n):=if n=0 then 1 else (2*binomial(2*n+1,n)+5*binomial(2*n-2,n+1))/(n+2); makelist(a(n),n,0,20); /* Tani Akinari, Jul 24 2025 */
Formula
a(n) = (2*binomial(2*n+1,n)+5*binomial(2*n-2,n+1))/(n+2) for n>0. - Tani Akinari, Jul 24 2025