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G. C. Greubel, <a href="/A073374/b073374.txt">Table of n, a(n) for n = 0..1000</a>

<a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,-30,15,81,-30,-120,0,80,32).

a(n) = sum(Sum_{k=0..n} b(k)*c(n-k), k=0..n) with b(k) := A001045(k+1) and c(k) := A073373(k).

a(n) = sumSum_{k=0..floor(n/2)} binomial(n-k+4, 4) * binomial(n-k, k) * 2^k, k=0..floor(n/2)).

a(n) = (5*(2968 +1974*n +411*n^2 +27*n^3)*(n+1)*U(n+1) + 2*(9412 +6099*n +1248*n^2 +81*n^3)*(n+2)*U(n))/(4!*3^7) with U(n) := A001045(n+1), n>=0.

G.f.: 1/(1-(1+2*x)*x)^5 = 1/((1+x)*(1-2*x))^5.

E.g.f.: (1/157464)*(512*(263 + 1104*x + 1026*x^2 + 306*x^3 + 27*x^4)*exp(2*x) + (22808 - 24432*x + 7344*x^2 - 792*x^3 + 27*x^4)*exp(-x)). - G. C. Greubel, Sep 29 2022

Table[(2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464, {n, 0, 40}] (* G. C. Greubel, Sep 29 2022 *)

(Magma) [(2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464: n in [0..40]]; // G. C. Greubel, Sep 29 2022

(SageMath)

def A073374(n): return (2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464

[A073374(n) for n in range(40)] # G. C. Greubel, Sep 29 2022

Cf. A001045, A073373.

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a(n) = sum(b(k)*c(n-k), k=0..n) with b(k) := A001045(k+1) and c(k) := A073373(k).

a(n) = sum(binomial(n-k+4, 4) * binomial(n-k, k) * 2^k, k=0..floor(n/2)).

a(n) = (5*(2968+1974*n+411*n^2+27*n^3)*(n+1)*U(n+1)+2*(9412+6099*n+1248*n^2 +81*n^3)*(n+2)*U(n))/(4!*3^7) with U(n) := A001045(n+1), n>=0.

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Wolfdieter Lang, Aug 2, 02 2002

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