A381877 G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^4, where C(x) is the g.f. of A000108.
1, 5, 36, 307, 2891, 29029, 304716, 3303712, 36708842, 415818822, 4783832314, 55743318579, 656528284027, 7802975428711, 93467830304056, 1127239608233884, 13676060532043690, 166800618473750824, 2043978275887704674, 25152767272402722288, 310703538187552229521
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(5*n-5*k+3, n-k)/(n+k+1));
Formula
a(n) = Sum_{k=0..n} binomial(n+k+1,k) * binomial(5*n-5*k+3,n-k)/(n+k+1).
a(n) = binomial(3 + 5*n, n)*hypergeom([-3/4-n, -1/2-n, -1/4-n, -n, 1+n], [-3/5-n, -2/5-n, -1/5-n, 1/5-n], 2^8/5^5)/(1 + n). - Stefano Spezia, Mar 09 2025