A395575 1 = Sum_{n>=0} a(n) * x^n * (1 - (n+1)*x)^(2*n+1).

1, 1, 6, 78, 1652, 49752, 1969122, 97329720, 5798325708, 405625348104, 32664538122378, 2981012062315032, 304446999573103104, 34436500081491536968, 4276838007390985310808, 578939457828472803556248, 84881510952427365778417596, 13405708766918088770485836168, 2269797643458376791801028026330

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..319

Formula

a(0) = 1; a(n) = Sum_{k=1..floor((2*n+1)/3)} (-1)^(k-1) * (n-k+1)^k * binomial(2*n-2*k+1,k) * a(n-k).

Prog

(PARI) a(n) = if(n==0, 1, sum(k=1, (2*n+1)\3, (-1)^(k-1)*(n-k+1)^k*binomial(2*n-2*k+1, k)*a(n-k)));

Crossrefs

Cf. A191459, A395574.

Sequence in context: A332680 A376093 A179498 * A393851 A177556 A219435

Adjacent sequences: A395572 A395573 A395574 * A395576 A395577 A395578

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2026

Status

approved