A390780 a(n) = (1/(5*n+4)) * Sum_{k=0..n} (5*k+4) * binomial(5*n+4,n-k).

1, 5, 36, 300, 2711, 25806, 254746, 2583408, 26748921, 281581835, 3004427056, 32418260592, 353128699929, 3877930871744, 42886340278416, 477207451335776, 5338880435729517, 60018633863615829, 677633185382734212, 7680486975714722460, 87359082462063990846, 996814112628754021092, 11407402559626117104204

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Formula

G.f.: g^4/(2-g) where g = 1+x*g^5 is the g.f. of A002294.

Mathematica

Table[Sum[(5*k+4)*Binomial[5*n+4, n-k]/(5*n+4), {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Nov 24 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (5*k+4)*binomial(5*n+4, n-k))/(5*n+4);
(Magma) [&+[(5*k+4)*Binomial(5*n+4, n-k)/(5*n+4): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 24 2025

Crossrefs

Cf. A304979, A390777, A390779.

Cf. A002294.

Sequence in context: A357153 A255489 A091161 * A388532 A364765 A135149

Adjacent sequences: A390777 A390778 A390779 * A390781 A390782 A390783

Keyword

nonn

Author

Seiichi Manyama, Nov 19 2025

Status

approved