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A370101
a(n) = Sum_{k=0..n} binomial(4*n,k) * binomial(4*n-k-1,n-k).
3
1, 7, 97, 1519, 25089, 427007, 7408897, 130287871, 2313945089, 41409732607, 745530884097, 13488086405119, 245014271688705, 4465915098890239, 81637668328243201, 1496095489290731519, 27477504726883368961, 505627095685486608383, 9320167322334416338945
OFFSET
0,2
FORMULA
a(n) = [x^n] ( (1+x)^4/(1-x)^3 )^n.
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x*(1-x)^3/(1+x)^4 ). See A365846.
PROG
(PARI) a(n) = sum(k=0, n, binomial(4*n, k)*binomial(4*n-k-1, n-k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 10 2024
STATUS
approved