A034835 Expansion of 1/(1-49*x)^(1/7); related to sept-factorial numbers A045754.

1, 7, 196, 6860, 264110, 10722866, 450360372, 19365495996, 847240449825, 37560993275575, 1682732498745760, 76028913806967520, 3459315578217022160, 158330213003009860400, 7283189798138453578400, 336483368673996555322080

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..445

A. Straub, V. H. Moll, T. Amdeberhan, The p-adic valuation of k-central binomial coefficients, Acta Arith. 140 (1) (2009) 31-41, eq (1.10)

Formula

a(n) = 7^n*A045754(n)/n!, n >= 1, A045754(n) = (7*n-6)(!^7) := product(7*j-6, j=1..n); G.f.: (1-49*x)^(-1/7).

D-finite with recurrence: n*a(n) +7*(-7*n+6)*a(n-1)=0. - R. J. Mathar, Jan 28 2020

Mathematica

CoefficientList[Series[1/(1 - 49*x)^(1/7), {x, 0, 50}], x] (* G. C. Greubel, Feb 22 2018 *)

Prog

(PARI) x='x+O('x^30); Vec(1/(1 - 49*x)^(1/7)) \\ G. C. Greubel, Feb 22 2018
(Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!(1/(1 - 49*x)^(1/7))) // G. C. Greubel, Feb 22 2018

Crossrefs

Cf. A045754, A004993, A034829, A034830, A034831, A034832, A034833, A034834.

Sequence in context: A182268 A156359 A128786 * A041371 A136675 A099198

Adjacent sequences: A034832 A034833 A034834 * A034836 A034837 A034838

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved