A378402 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+3*k,n).
1, 5, 49, 533, 6081, 71365, 853105, 10331221, 126321409, 1556044805, 19280812849, 240054516245, 3000687934401, 37634567169477, 473365023172209, 5968699720282453, 75422513665403905, 954877942305602053, 12109526474814388273, 153801537443722913813, 1956059583033416379841
Offset: 0
Keywords
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..898
Programs
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Mathematica
Table[Sum[Binomial[n,k]Binomial[n+3k,n],{k,0,n}],{n,0,20}] (* Harvey P. Dale, Nov 27 2024 *) -
PARI
a(n) = sum(k=0, n, binomial(n, k)*binomial(n+3*k, n));
Formula
a(n) = [x^n] (1 + x + (1 + x)^4)^n.