A156928 G.f. of the z^1 coefficients of the FP1 in the second column of the A156921 matrix.

1, 7, 28, 86, 227, 545, 1230, 2664, 5613, 11611, 23728, 48106, 97031, 195077, 391394, 784284, 1570353, 3142815, 6288100, 12579070, 25161451, 50326697, 100657718, 201320336, 402646197, 805298595

Offset

2,2

Comments

Antidiagonal sums of the convolution array A213582. - Clark Kimberling, Jun 19 2012

Links

G. C. Greubel, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-9,2).

Formula

a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) + 2.

a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 9*a(n-4) + 2*a(n-5).

a(n) = (9*2^(n+2) - (2*n^3 + 9*n^2 + 25*n + 36))/6.

G.f.: GF3(z;m=1) = z^2*(1+z)/((1-z)^4*(1-2*z)).

a(n) = Sum_{k=1..n+1} Sum_{i=1..n+1} (k-1)^2 * C(n-k+1,i). - Wesley Ivan Hurt, Sep 22 2017

E.g.f.: (36*exp(2*x) - (36 + 36*x + 15*x^2 + 2*x^3)*exp(x))/6. - G. C. Greubel, Jul 08 2019

Mathematica

Table[(9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6, {n, 2, 40}] (* Michael De Vlieger, Sep 23 2017 *)

Prog

(PARI) vector(40, n, n++; (9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6) \\ G. C. Greubel, Jul 08 2019
(Magma) [(9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6: n in [2..40]]; // G. C. Greubel, Jul 08 2019
(Sage) [(9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6 for n in (2..40)] # G. C. Greubel, Jul 08 2019
(GAP) List([2..40], n-> (9*2^(n+2) -(2*n^3+9*n^2+25*n+36))/6) # G. C. Greubel, Jul 08 2019

Crossrefs

Cf. A156927.

Equals second column of A156921.

Other columns A156929, A156930, A156931.

Sequence in context: A144900 A054469 A369806 * A117473 A163037 A224153

Adjacent sequences: A156925 A156926 A156927 * A156929 A156930 A156931

Keyword

easy,nonn

Author

Johannes W. Meijer, Feb 20 2009

Status

approved