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A156928 G.f. of the z^1 coefficients of the FP1 in the second column of the A156921 matrix. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A221141 A144900 A054469 * A117473 A163037 A224153

Adjacent sequences:  A156925 A156926 A156927 * A156929 A156930 A156931

KEYWORD

easy,nonn

AUTHOR

Johannes W. Meijer, Feb 20 2009

STATUS

approved

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Last modified May 6 15:14 EDT 2021. Contains 343586 sequences. (Running on oeis4.)