A308804 Triangular table of coefficients of p in p^(k+2)/(1-p) LerchPhi(1-p,-1-k,(p-1)/p) as function of k=1..n.

1, 2, -1, 9, -9, 1, 44, -66, 24, -1, 265, -530, 320, -55, 1, 1854, -4635, 3940, -1275, 118, -1, 14833, -44499, 48825, -23485, 4571, -245, 1, 133496, -467236, 628544, -403270, 123368, -15400, 500, -1, 1334961, -5339844, 8510376, -6841674, 2885694, -598416, 49914, -1011, 1, 14684570, -66080565, 121759560, -117782490, 63630588, -18808230, 2752320, -157785, 2034, -1

Offset: 1

Author

Wouter Meeussen, Jun 25 2019

Keywords

• sign
• tabl

Comments

Relations to other sequences are tentative (checked up to 24 rows). Related to the central moments of a geometric probability distribution.

Each row sums to 1. Row sums of absolute values are A091346. First column is A000166. First moments appear to be A052515 with shifted index.

Links

• Wolfram Language & System Documentation Center, LerchPhi (then click in Applications).

Crossrefs

Cf. A091346, A000166, A052515.

Programs

Mathematica

Table[CoefficientList[ p^(k + 2)/(1 - p) LerchPhi[1 - p, -k - 1, (-1 + p)/p], p], {k, 1, 12}]