A396244 Expansion of 1 / (1 - B(B(x))), where B(x) = x/(1-x)^4.

1, 1, 9, 69, 497, 3471, 23913, 163843, 1120361, 7656486, 52318487, 357514990, 2443171893, 16696623338, 114106843007, 779828040814, 5329516155813, 36423140201867, 248924239329266, 1701206464309672, 11626442430613559, 79457820305840230, 543033266143895110

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (21, -186, 942, -3105, 7203, -12404, 16400, -16998, 13963, -9114, 4698, -1880, 565, -120, 16, -1).

Formula

G.f.: ((1-x)^4 - x)^4 / (((1-x)^4 - x)^4 - x*(1-x)^12).

a(n) = 21*a(n-1) - 186*a(n-2) + 942*a(n-3) - 3105*a(n-4) + 7203*a(n-5) - 12404*a(n-6) + 16400*a(n-7) - 16998*a(n-8) + 13963*a(n-9) - 9114*a(n-10) + 4698*a(n-11) - 1880*a(n-12) + 565*a(n-13) - 120*a(n-14) + 16*a(n-15) - a(n-16) for n > 16.

a(0) = 1; a(n) = Sum_{i=1..n} Sum_{j=1..i} binomial(n+3*i-1,4*i-1) * binomial(i+3*j-1,4*j-1).

Prog

(PARI) a(n) = if(n==0, 1, sum(i=1, n, sum(j=1, i, binomial(n+3*i-1, 4*i-1)*binomial(i+3*j-1, 4*j-1))));

Crossrefs

Cf. A055991, A396208, A396245.

Sequence in context: A297593 A198691 A125372 * A165147 A075045 A361139

Adjacent sequences: A396241 A396242 A396243 * A396245 A396246 A396247

Keyword

nonn

Author

Seiichi Manyama, May 20 2026

Status

approved