A097790 -id:A097790 - cp's OEIS frontend

A097791 a(n)=5a(n-1)+C(n+4,4),n>0, a(0)=1.

1, 10, 65, 360, 1870, 9476, 47590, 238280, 1191895, 5960190, 29801951, 149011120, 745057420, 3725289480, 18626450460, 93132256176, 465661285725, 2328306434610, 11641532180365, 58207660910680, 291038304564026

Offset: 0

Paul Barry, Aug 24 2004

Partial sums of A097790.

Index entries for linear recurrences with constant coefficients, signature (10,-35,60,-55,26,-5).

G.f.: 1/((1-5*x)*(1-x)^5).
a(n) = 5^(n+5)/1024-(32*n^4+480*n^3+2680*n^2+6660*n+6303)/3072.
a(n) = Sum_{k=0..n} binomial(n+5, k+5)*4^k.

A229702 Expansion of 1/((1-x)^4*(1-6x)).

Original entry on oeis.org

1, 10, 70, 440, 2675, 16106, 96720, 580440, 3482805, 20897050, 125382586, 752295880, 4513775735, 27082654970, 162495930500, 974975583816, 5849853503865, 35099121024330, 210594726147310, 1263568356885400, 7581410141314171

Offset: 0

Yahia Kahloune, Sep 27 2013

This sequence was chosen to illustrate a way to match generating functions and closed-form solutions.
The general term associated with the generating function
1/((1-s*x)^4*(1-r*x)) with r>s>=1 is a(n) = [ r^(n+4) - s^(n+1)*(s^3 + s^2*(r-s)*binomial(n+4,1) + s*(r-s)^2*binomial(n+4,2)+(r-s)^3*binomial(n+4,3))]/(r-s)^4.

			a(3) = (6^8 - (125*3^3  + 1200*3^2 + 3805*3 + 4026))/3750 = 440.

Index entries for linear recurrences with constant coefficients, signature (10,-30,40,-25,6).

Cf. A002663, A097786, A097788, A097790.

a(n) = (6^(n+4) - (1 + 5*C(n+4,1) + 25*C(n+4,2) + 125*C(n+4,3)))/625 = (6^(n+5) - (125*n^3 + 1200*n^2 + 3805*n + 4026))/3750.

cp's OEIS Frontend

A097791 a(n)=5a(n-1)+C(n+4,4),n>0, a(0)=1.

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