A370101 a(n) = Sum_{k=0..n} binomial(4*n,k) * binomial(4*n-k-1,n-k).

1, 7, 97, 1519, 25089, 427007, 7408897, 130287871, 2313945089, 41409732607, 745530884097, 13488086405119, 245014271688705, 4465915098890239, 81637668328243201, 1496095489290731519, 27477504726883368961, 505627095685486608383, 9320167322334416338945

Offset

0,2

Links

Table of n, a(n) for n=0..18.

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

Cf. A001448, A370100, A370102.

Cf. A365846.

Sequence in context: A243867 A232290 A011943 * A218669 A371367 A188441

Adjacent sequences: A370098 A370099 A370100 * A370102 A370103 A370104

Keyword

nonn

Author

Seiichi Manyama, Feb 10 2024

Status

approved