A383634 Expansion of 1/( Product_{k=0..3} (1 - (4*k+1) * x) ).

1, 28, 530, 8540, 126651, 1791048, 24604420, 331842280, 4422301301, 58467523268, 768888466710, 10074907080420, 131688310339951, 1718380224948688, 22396840268491400, 291680037734786960, 3796530709486682601, 49397112147411259308, 642542379001477422490, 8356470240627243865900

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (28,-254,812,-585).

Formula

a(n) = Sum_{k=0..n} 4^k * binomial(n+3,k+3) * Stirling2(k+3,3).

a(n) = (13^(n+3) - 3*9^(n+3) + 3*5^(n+3) - 1)/384.

a(n) = 28*a(n-1) - 254*a(n-2) + 812*a(n-3) - 585*a(n-4).

G.f.: B(x)^4, where B(x) is the g.f. of A383628.

a(n) = Sum_{k=0..n} (-4)^k * 13^(n-k) * binomial(n+3,k+3) * Stirling2(k+3,3).

Prog

(PARI) a(n) = (13^(n+3)-3*9^(n+3)+3*5^(n+3)-1)/384;

Crossrefs

Cf. A383628.

Sequence in context: A020973 A023947 A020972 * A025957 A020758 A022000

Adjacent sequences: A383631 A383632 A383633 * A383635 A383636 A383637

Keyword

nonn,easy

Author

Seiichi Manyama, May 03 2025

Status

approved