A153757 a(n) = Sum_{k=1..n} A003266(k).

1, 2, 4, 10, 40, 280, 3400, 68920, 2296600, 124819000, 11029312600, 1581276391000, 367448845658200, 138299522459392600, 84276864426837376600, 83129040425047907584600, 132705616446736897029760600, 342829213074356555028732544600

Offset

1,2

Comments

Equals A000012 * A003266, where A000012 = the partial sum operator as an infinite lower triangular matrix.

a(n)+1 is divisible by 149 (a prime factor of Fibonacci(37)) for all n >= 36. The only values of n for which a(n)+1 is prime are: 1, 2, 3, 4, 5, 6, 10, 18. The corresponding primes are: 2, 3, 5, 11, 41, 281, 124819001, 342829213074356555028732544601. - Amiram Eldar, May 04 2017

Links

Table of n, a(n) for n=1..18.

Formula

Partial sums of A003266 terms.

Example

a(4) = 10 = (1 + 1 + 2 + 6), where A003266 = (1, 1, 2, 6, 30, 240, 3120,...).

Mathematica

a[n_]:=Sum[Fibonorial[k], {k, n}]; Table[a[n], {n, 1, 10}]

Crossrefs

Cf. A003266, A153758 (partial sums).

Sequence in context: A086852 A084737 A322698 * A159860 A013549 A184253

Adjacent sequences: A153754 A153755 A153756 * A153758 A153759 A153760

Keyword

nonn

Author

Gary W. Adamson, Dec 31 2008

Extensions

More terms from Amiram Eldar, Feb 26 2020

Status

approved