A115204 Seventh column of triangle A115193 (called C(1,2)).

1, 13, 123, 1037, 8291, 64509, 494595, 3761661, 28486659, 215277565, 1625688067, 12277764093, 92783468547, 701828038653, 5314762113027, 40297495658493, 305941006516227, 2325794003091453, 17704219384479747

Offset

0,2

Comments

Also sixth diagonal of triangle A115195, called Y(1,2), divided by 32.

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Formula

a(n) = A115195(5+n,1+n)/32, n>=0.

G.f.: (-1 + 7*x - 8*x^2 + (1- 9*x + 18*x^2 - 4*x^3)*c(2*x))/(16*(1+x)*x^5), with the o.g.f. c(x) of A000108 (Catalan).

G.f. is also: ((1 + 2*x*c(2*x))*(2*x*c(2*x))^6)/(64*(1+x)*x^6).

a(n) = A115193(6+n,6), n>=0.

a(n) = (-1)^n*2^(8+3*n)*(Binomial[1/2, 4 + n]*Hypergeometric2F1[1, 7/2 + n, 5 + n, -8] + 4*(9*Binomial[1/2, 5 + n]*Hypergeometric2F1[1, 9/2 + n, 6 + n, -8] + 36*Binomial[1/2, 6 + n]*Hypergeometric2F1[1, 11/2 + n, 7 + n, -8] + 32*Binomial[1/2, 7 + n]*Hypergeometric2F1[1, 13/2 + n, 8 + n, -8])). - G. C. Greubel, Feb 04 2016

D-finite with recurrence 2*n*(n+6)*a(n) +(-11*n^2-51*n-120)*a(n-1) +(-37*n^2-99*n-132)*a(n-2) -12*(n+1)*(2*n+1)*a(n-3)=0. - R. J. Mathar, Mar 10 2022

Mathematica

f[n_] := SeriesCoefficient[(1 - 13*x + 46*x^2 - 36*x^3 -(1 - 9*x + 18*x^2 - 4*x^3) Sqrt[1 - 8*x])/(64*x^6*(1 + x)), {x, 0, n}];
Table[f[n], {n, 0, 50}] (* G. C. Greubel, Feb 04 2016 *)

Crossrefs

Cf. A000108, A115202, A115203.

Sequence in context: A201382 A101186 A295778 * A016277 A202131 A152583

Adjacent sequences: A115201 A115202 A115203 * A115205 A115206 A115207

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 03 2006

Status

approved