A383911 Expansion of Product_{k=0..4} (1 + k*x)/(1 - k*x).

1, 20, 200, 1400, 8000, 40520, 190400, 852200, 3692000, 15640520, 65225600, 268985000, 1100372000, 4475152520, 18122340800, 73156029800, 294627068000, 1184523016520, 4756148096000, 19078784066600, 76477758500000, 306398995072520, 1227060052251200, 4912632802375400, 19663709744588000

Offset: 0

Author

Seiichi Manyama, May 14 2025

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Crossrefs

Column k=4 of A383900.

Cf. A383913.

Programs

PARI

a(n) = if(n==0, 1, 70*4^n-140*3^n+45*2^(n+1)-20);

Formula

a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4) for n > 4.

a(n) = Sum_{k=0..4} |Stirling1(5,k+1)| * Stirling2(k+n,4).

a(n) = A383913(n) + 4*A383913(n-1) = 70*4^n - 140*3^n + 45*2^(n+1) - 20 for n > 0.