A381861 G.f. A(x) satisfies A(x) = (1 + x*A(x))^4 * C(x), where C(x) is the g.f. of A000108.
1, 5, 32, 231, 1797, 14715, 125064, 1093194, 9766783, 88793815, 818832674, 7640868924, 72014955566, 684551660324, 6555290711728, 63179148757584, 612376024087047, 5965515657187437, 58375460484257734, 573545171374958628, 5655759227878768987, 55957005428512022905
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(4*n-4*k+4, n-k)/(n+k+1));
Formula
a(n) = Sum_{k=0..n} binomial(n+k+1,k) * binomial(4*n-4*k+4,n-k)/(n+k+1).
a(n) = binomial(4 + 4*n, n)*hypergeom([-4/3-n, -2/3-n, -n, 1+n], [-3/4-n, -1/2-n, -1/4-n], 3^3/2^8)/(1 + n). - Stefano Spezia, Mar 09 2025