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

1,2

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

Table of n, a(n) for n=1..55.

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

Mathematica

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

Crossrefs

Cf. A091346, A000166, A052515.

Sequence in context: A230358 A228721 A108290 * A364709 A108291 A019615

Adjacent sequences: A308801 A308802 A308803 * A308805 A308806 A308807

Keyword

sign,tabl

Author

Wouter Meeussen, Jun 25 2019

Status

approved