A259455 n Sum_n Sum_n Sum_n.

1, 30, 270, 1400, 5250, 15876, 41160, 95040, 200475, 393250, 726726, 1277640, 2153060, 3498600, 5508000, 8434176, 12601845, 18421830, 26407150, 37191000, 51546726, 70409900, 94902600, 126360000, 166359375, 216751626, 279695430, 357694120, 453635400, 570834000

Offset

1,2

Comments

See the reference for an explanation of the rather cryptic definition.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

C. Krishnamachari, The operator (xD)^n, J. Indian Math. Soc., 15 (1923), 3-4. [Annotated scanned copy]

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

From Alois P. Heinz, Jul 04 2015: (Start)

G.f.: (24*x^3+58*x^2+22*x+1)*x/(x-1)^8.

a(n) = n^3*(n+3)*(n+2)*(n+1)^2/48.

a(n) = n*Stirling2(n+3,n). (End)

From Amiram Eldar, Nov 02 2025: (Start)

Sum_{n>=1} 1/a(n) = 1841/27 - 70*Pi^2/9 + 8*zeta(3).

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/9 + 640*log(2)/9 + 6*zeta(3) - 1529/27. (End)

Maple

a:= n-> n^3*(n+3)*(n+2)*(n+1)^2/48:
seq(a(n), n=1..40);  # Alois P. Heinz, Jul 04 2015

Crossrefs

This is the seventh sequence in the sequence A000027, A000217, A002411, A001296, A108650, A001297, ...

Sequence in context: A053358 A163667 A214944 * A270852 A229427 A113754

Adjacent sequences: A259452 A259453 A259454 * A259456 A259457 A259458

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 30 2015

Extensions

More terms from Alois P. Heinz, Jul 04 2015

Status

approved