A390743 a(n) = Sum_{k=0..n} (-1)^k * (3*k+1) * binomial(5*n-2*k+1,n-k)/(5*n-2*k+1).

1, 0, 2, 15, 128, 1166, 11129, 109911, 1114030, 11523655, 121168956, 1291306328, 13916949253, 151423573995, 1661086662123, 18351468264991, 204007736896808, 2280364339319773, 25614171406057695, 288970057622756380, 3272901580227404376, 37201338713751214738

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..920

Formula

G.f.: g/(1+x*g^3) where g = 1+x*g^5 is the g.f. of A002294.

Mathematica

Table[Sum[(-1)^k*(3*k+1)*Binomial[5*n -2*k+1, n-k]/(5*n-2*k+1), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 17 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*(3*k+1)*binomial(5*n-2*k+1, n-k)/(5*n-2*k+1));
(Magma) [&+[(-1)^k*(3*k+1)*Binomial(5*n-2*k+1, n-k)/(5*n-2*k+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 17 2025

Crossrefs

Cf. A390741, A390742, A390744.

Cf. A002294, A390712.

Sequence in context: A396557 A051407 A371580 * A242091 A132182 A365151

Adjacent sequences: A390740 A390741 A390742 * A390744 A390745 A390746

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2025

Status

approved