A396241 Expansion of 1 / (1 - B(B(B(x)))), where B(x) = x/(1-x)^2.

1, 1, 7, 46, 295, 1868, 11746, 73566, 459701, 2868839, 17890042, 111514170, 694931568, 4330050997, 26977960626, 168075845641, 1047104723691, 6523316303432, 40639003178173, 253171922034855, 1577200193353582, 9825562314051139, 61210737601514136, 381327026058717406

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (15,-83,220,-303,220,-83,15,-1).

Formula

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

a(n) = 15*a(n-1) - 83*a(n-2) + 220*a(n-3) - 303*a(n-4) + 220*a(n-5) - 83*a(n-6) + 15*a(n-7) - a(n-8) for n > 8.

a(0) = 1; a(n) = Sum_{i=1..n} Sum_{j=1..i} Sum_{k=1..j} binomial(n+i-1,2*i-1) * binomial(i+j-1,2*j-1) * binomial(j+k-1,2*k-1).

Prog

(PARI) a(n) = if(n==0, 1, sum(i=1, n, sum(j=1, i, sum(k=1, j, binomial(n+i-1, 2*i-1)*binomial(i+j-1, 2*j-1)*binomial(j+k-1, 2*k-1)))));

Crossrefs

Cf. A088305, A289803, A396238.

Sequence in context: A264201 A086092 A081894 * A128597 A387008 A190972

Adjacent sequences: A396238 A396239 A396240 * A396242 A396243 A396244

Keyword

nonn

Author

Seiichi Manyama, May 20 2026

Status

approved