OFFSET
1,2
COMMENTS
Inspired by doubly triangular numbers (A002817).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..226
FORMULA
a(n) = Sum_{i=1..n} Product_{j=T(i-1)+1..T(i)} j where T(n) is n-th triangular number.
a(n) = A227364(T(n)) where T(n) is n-th triangular number.
a(n) ~ n^(2*n) / 2^n. - Vaclav Kotesovec, Nov 20 2021
EXAMPLE
a(2) = 1 + 2*3 = 7.
a(3) = 1 + 2*3 + 4*5*6 = 127.
a(4) = 1 + 2*3 + 4*5*6 + 7*8*9*10 = 5167.
MATHEMATICA
Accumulate @ Table[(n * (n + 1)/2)!/((n - 1) * n /2)!, {n, 1, 16}] (* Amiram Eldar, Jul 23 2020 *)
PROG
(PARI) {a(n) = sum(i=1, n, prod(j=(i-1)*i/2+1, i*(i+1)/2, j))}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jul 23 2020
STATUS
approved