A356813
Expansion of e.g.f. exp(x * (1 - exp(3*x))).
Original entry on oeis.org
1, 0, -6, -27, 0, 1215, 12312, 45927, -657072, -15857937, -167699160, -266960529, 29356170984, 700068823623, 8419188469104, -1491045413265, -2856006296224992, -79065447339366945, -1162293393139510824, -744123842820101745, 538503788896323210360
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(1-exp(3*x)))))
-
my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k/(1-(3*k+1)*x)^(k+1)))
-
a(n) = sum(k=0, n, (-1)^k*(3*k+1)^(n-k)*binomial(n, k));
-
a(n) = n!*sum(k=0, n\2, (-1)^k*3^(n-k)*stirling(n-k, k, 2)/(n-k)!);
A356815
Expansion of e.g.f. exp(-x * (exp(2*x) + 1)).
Original entry on oeis.org
1, -2, 0, 4, 32, 48, -608, -6400, -24064, 163072, 3567104, 28394496, 6535168, -3250745344, -50725740544, -344530853888, 2476610551808, 110057610608640, 1655672654135296, 9616664975114240, -195178079811272704, -6998474114188967936, -110894925369151848448
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(exp(2*x)+1))))
-
my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k/(1-(2*k-1)*x)^(k+1)))
-
a(n) = sum(k=0, n, (-1)^k*(2*k-1)^(n-k)*binomial(n, k));
A356818
Expansion of e.g.f. exp(-x * (exp(x) + 1)).
Original entry on oeis.org
1, -2, 2, 1, 0, -17, -32, 103, 976, 2287, -12816, -143585, -481016, 2339335, 39769720, 209863327, -397553376, -16949434913, -142681662368, -233212601153, 9138353475736, 128343346833463, 702261255539496, -4251314594919617, -135331386127555856
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(exp(x)+1))))
-
my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k/(1-(k-1)*x)^(k+1)))
-
a(n) = sum(k=0, n, (-1)^k*(k-1)^(n-k)*binomial(n, k));
A356817
a(n) = Sum_{k=0..n} (-1)^k * (k*n-1)^(n-k) * binomial(n,k).
Original entry on oeis.org
1, -2, 0, 1, 144, 4143, 110368, 2535475, 13299968, -5169863825, -639341093376, -59073970497885, -4677854594527232, -276406098219258425, 2399871442122924032, 5163244810691492730907, 1331213942683118587674624, 262517264591996332314037215
Offset: 0
Showing 1-4 of 4 results.