A383635 Expansion of 1/( Product_{k=0..4} (1 - (5*k+1) * x) ).

1, 55, 1940, 56210, 1461495, 35567301, 829147810, 18774611680, 416583297845, 9111004217315, 197197849460976, 4235712944853390, 90470493402792595, 1924292232588575905, 40801645704191871710, 863108809168841357276, 18225784176922532902545

Offset: 0

Author

Seiichi Manyama, May 03 2025

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (55,-1085,9185,-30330,22176).

Crossrefs

Cf. A383629.

Programs

PARI

a(n) = (21^(n+4)-4*16^(n+4)+6*11^(n+4)-4*6^(n+4)+1)/15000;

Formula

a(n) = Sum_{k=0..n} 5^k * binomial(n+4,k+4) * Stirling2(k+4,4).

a(n) = (21^(n+4) - 4*16^(n+4) + 6*11^(n+4) - 4*6^(n+4) + 1)/15000.

a(n) = 55*a(n-1) - 1085*a(n-2) + 9185*a(n-3) - 30330*a(n-4) + 22176*a(n-5).

G.f.: B(x)^5, where B(x) is the g.f. of A383629.

a(n) = Sum_{k=0..n} (-5)^k * 21^(n-k) * binomial(n+4,k+4) * Stirling2(k+4,4).