A381916 Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / B(x) ), where B(x) is the g.f. of A002293.

1, 4, 29, 270, 2897, 34051, 426199, 5582619, 75660075, 1052748518, 14956346820, 216088986290, 3165555750458, 46912569559556, 702072705679590, 10595488626535181, 161071258091631337, 2464201011094137000, 37911236702465987337, 586166246311185676045, 9103432675706477369934

Offset: 0

Author

Seiichi Manyama, Mar 10 2025

Keywords

• nonn

Crossrefs

Cf. A381914, A381915.

Cf. A381880, A381913.

Cf. A002293.

Programs

PARI

a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(4*n-k+2, n-k)/(n+4*k+1));

Formula

G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x*A(x))^3.

a(n) = Sum_{k=0..n} binomial(n+4*k+1,k) * binomial(4*n-k+2,n-k)/(n+4*k+1).