A352864 -id:A352864 - cp's OEIS frontend

A352865 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-k,k) * a(n-2*k-1).

1, 1, 1, -1, -4, -5, 6, 36, 46, -101, -515, -506, 2554, 9991, 3067, -79915, -227056, 205681, 2841708, 5134140, -18296153, -107927240, -66578269, 1174691649, 4059143386, -4667894370, -69377504739, -126787267800, 669710503012, 3835079736835, 475781902203

Offset: 0

Ilya Gutkovskiy, Apr 06 2022

sign

Cf. A014619, A172385, A352864.

a[0] = 1; a[n_] := a[n] = Sum[(-1)^k Binomial[n - k, k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 30}]
nmax = 30; A[] = 0; Do[A[x] = 1 + x A[x/(1 + x^2)]/(1 + x^2)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]

G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 + x^2)) / (1 + x^2)^2.

A360892 G.f. satisfies A(x) = 1 + x/(1 - x^3)^2 * A(x/(1 - x^3)).

Original entry on oeis.org

1, 1, 1, 1, 3, 6, 10, 18, 42, 94, 193, 428, 1036, 2470, 5779, 14192, 36176, 91649, 233617, 613978, 1641492, 4396393, 11922501, 32969768, 92080274, 258774392, 736441673, 2123145058, 6168831095, 18067587851, 53493963264, 159884523503, 481343585105, 1461055679181

Offset: 0

Seiichi Manyama, Feb 25 2023

nonn

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

Cf. A040027, A352864, A360893.

Cf. A360890, A360900.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\3, binomial(i-2*j, j)*v[i-3*j])); v;

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

A360893 G.f. satisfies A(x) = 1 + x/(1 - x^4)^2 * A(x/(1 - x^4)).

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 6, 10, 15, 24, 51, 109, 214, 389, 747, 1595, 3497, 7379, 15065, 31750, 70504, 159352, 353748, 777240, 1742696, 4022595, 9379659, 21717264, 50239529, 117913537, 281584044, 676667552, 1623733085, 3908144320, 9509212539, 23393422297, 57815808829

Offset: 0

Seiichi Manyama, Feb 25 2023

nonn

Cf. A040027, A352864, A360892.

Cf. A360891, A360901.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\4, binomial(i-3*j, j)*v[i-4*j])); v;

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n-3*k,k) * a(n-1-4*k).

cp's OEIS Frontend

A352865 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-k,k) * a(n-2*k-1).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A360892 G.f. satisfies A(x) = 1 + x/(1 - x^3)^2 * A(x/(1 - x^3)).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A360893 G.f. satisfies A(x) = 1 + x/(1 - x^4)^2 * A(x/(1 - x^4)).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula