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A190724 Row sums of Riordan matrix A118384. 1
1, 4, 20, 106, 576, 3174, 17648, 98746, 555104, 3131854, 17720880, 100507554, 571179792, 3251459670, 18535914480, 105803208906, 604598535360, 3458315246238, 19799128470896, 113441876080306, 650450158678256, 3731985710892454, 21425304596140080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n) = (6^n+d(n)-sum(6^(k-1)*d(n-k),k=1..n))/2, where d(n) = central Delannoy number (A001850).

G.f.: (1-7*x+sqrt(1-6*x+x^2))/((2-12*x)*sqrt(1-6*x+x^2)).

Recurrence: (n^2+9*n+20)*a(n+5)-8*(3*n^2+23*n+44)*a(n+4)+2*(108*n^2+683*n+1089)*a(n+3)-2*(435*n^2+2159*n+2716)*a(n+2)+(1367*n^2+4917*n+4366)*a(n+1)-210*(n^2+3*n+2)*a(n)=0.

Conjecture: n*(2*n+3)*a(n) +2*(-12*n^2-15*n+22)*a(n-1) +(74*n^2+73*n-274)*a(n-2) -6*(2*n+5)*(n-2)*a(n-3)=0. - R. J. Mathar, Jul 24 2012

a(n) ~ (2+sqrt(2))/(2*sqrt(3*sqrt(2)-4)) * (3+2*sqrt(2))^n/sqrt(Pi*n). - Vaclav Kotesovec, Oct 20 2012

MATHEMATICA

CoefficientList[Series[(1-7x+Sqrt[1-6x+x^2])/((2-12x)Sqrt[1-6x+x^2]), {x, 0, 100}], x]

PROG

(PARI) x='x+O('x^50); Vec((1-7*x+sqrt(1-6*x+x^2))/((2-12*x)*sqrt(1-6*x+x^2))) \\ G. C. Greubel, Mar 26 2017

CROSSREFS

Cf. A001850, A118384.

Sequence in context: A061709 A254537 A135159 * A243585 A263965 A265084

Adjacent sequences:  A190721 A190722 A190723 * A190725 A190726 A190727

KEYWORD

nonn

AUTHOR

Emanuele Munarini, May 17 2011

STATUS

approved

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Last modified June 25 18:38 EDT 2022. Contains 354851 sequences. (Running on oeis4.)