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URL: https://oeis.org/A388531

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A388531
Coefficient of x^n in the expansion of ( (1+x)^5 + x^2 )^n.
4
1, 5, 47, 485, 5271, 58980, 672545, 7771062, 90674175, 1065986117, 12606912022, 149819960680, 1787614252449, 21401583775785, 256963361581848, 3092992216987635, 37310463035800975, 450934394707330291, 5459249623120215995, 66192758345153315101, 803672389181041746046
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(5*n-5*k,n-2*k).
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / ((1+x)^5 + x^2) ). See A388532.
MATHEMATICA
Table[SeriesCoefficient[Series[((1+t)^5+t^2)^n, {t, 0, n}], n], {n, 0, 20}] (* Vincenzo Librandi, Sep 27 2025 *)
PROG
(PARI) a(n) = sum(k=0, n\2, binomial(n, k)*binomial(5*n-5*k, n-2*k));
(Magma) R<t> := PolynomialRing(Integers()); seq := [ MonomialCoefficient(((1+t)^5 + t^2)^n, t^n) : n in [0..20] ]; seq; // Vincenzo Librandi, Sep 27 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 18 2025
STATUS
approved