A277353 a(n) = Product_{k=1..n} (3*k^2+1).

1, 4, 52, 1456, 71344, 5422144, 591013696, 87470027008, 16881715212544, 4119138511860736, 1239860692070081536, 451309291913509679104, 195416923398549691052032, 99271797086463243054432256, 58471088483926850159060598784, 39526455815134550707524964777984

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

a(n) ~ 2*3^(n+1/2) * n^(2*n+1) * sinh(Pi/sqrt(3)) / exp(2*n).

Mathematica

Table[Product[3*k^2+1, {k, 1, n}], {n, 0, 15}]

Prog

(Python)
from math import prod
def A277353(n): return prod(3*k**2+1 for k in range(1, n+1)) # Aidan Chen, Feb 13 2026

Crossrefs

Cf. A101686, A277352, A277354.

Sequence in context: A343429 A395386 A382676 * A055974 A009671 A015001

Adjacent sequences: A277350 A277351 A277352 * A277354 A277355 A277356

Keyword

nonn

Author

Vaclav Kotesovec, Oct 10 2016

Status

approved