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A336502 Partial sums of A057003. 2
1, 7, 127, 5167, 365527, 39435607, 6006997207, 1226103906007, 322796982334807, 106460296033918807, 42980408446129381207, 20846482682939051365207, 11959807608801430284133207, 8010447502346968140207973207, 6193994326661240674349352805207, 5476021766725276671842502543205207 (list; graph; refs; listen; history; text; internal format)
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

Cf. A000217, A002817, A007489, A057003, A227364, A336513.

Sequence in context: A092676 A002067 A274571 * A138523 A034670 A020516

Adjacent sequences:  A336499 A336500 A336501 * A336503 A336504 A336505

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Jul 23 2020

STATUS

approved

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Last modified August 7 16:00 EDT 2022. Contains 355994 sequences. (Running on oeis4.)