A378551 a(n) = Sum_{k=0..n} 4^k * binomial(n/2+k-1,k) * binomial(n-1,n-k).
1, 2, 20, 206, 2200, 24062, 267500, 3009050, 34150000, 390265190, 4484762500, 51771831146, 599921125000, 6974108163778, 81297715937500, 949957147566086, 11123368187500000, 130487420114543110, 1533247106445312500, 18042303960492212810, 212590835968046875000
Offset: 0
Keywords
Programs
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Mathematica
a[n_]:=SeriesCoefficient[ 1/(1 - 4*x/(1-x))^(n/2),{x,0,n}]; Array[a,21,0] (* Stefano Spezia, Nov 30 2024 *) -
PARI
a(n) = sum(k=0, n, 4^k*binomial(n/2+k-1, k)*binomial(n-1, n-k));
Formula
a(n) = [x^n] 1/(1 - 4*x/(1-x))^(n/2).