A308804 - OEIS

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.

%I #14 Jun 25 2019 16:56:12

%S 1,2,-1,9,-9,1,44,-66,24,-1,265,-530,320,-55,1,1854,-4635,3940,-1275,

%T 118,-1,14833,-44499,48825,-23485,4571,-245,1,133496,-467236,628544,

%U -403270,123368,-15400,500,-1,1334961,-5339844,8510376,-6841674,2885694,-598416,49914,-1011,1,14684570,-66080565,121759560,-117782490,63630588,-18808230,2752320,-157785,2034,-1

%N 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.

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

%C 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.

%H Wolfram Language & System Documentation Center, <a href="https://reference.wolfram.com/language/ref/LerchPhi.html">LerchPhi</a> (then click in Applications).

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

%Y Cf. A091346, A000166, A052515.

%K sign,tabl

%O 1,2

%A _Wouter Meeussen_, Jun 25 2019