A368585
a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k+2,3) / k!.
Original entry on oeis.org
0, 1, 2, 4, 4, 15, -34, 322, -2456, 22269, -222470, 2447456, -29369108, 381798859, -5345183466, 80177752670, -1282844041904, 21808348713337, -392550276838926, 7458455259940924, -149169105198816940, 3132551209175157511, -68916126601853463218
Offset: 0
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my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 2, binomial(2, k)*x^k/(k+1)!)*exp(x)/(1+x))))
A368586
a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k+3,4) / k!.
Original entry on oeis.org
0, 1, 3, 6, 11, 15, 36, -42, 666, -5499, 55705, -611754, 7342413, -95449549, 1336296066, -20044437930, 320711010756, -5452087178007, 98137569210111, -1864613814984794, 37292276299704735, -783137802293788809, 17229031650463366448, -396267727960657413354
Offset: 0
-
my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 3, binomial(3, k)*x^k/(k+1)!)*exp(x)/(1+x))))
A368718
a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * k^5 / k!.
Original entry on oeis.org
0, 1, 30, 153, 412, 1065, 1386, 7105, -24072, 275697, -2656970, 29387721, -352403820, 4581620953, -64142155518, 962133092145, -15394128425744, 261700184657505, -4710603321945522, 89501463119441017, -1790029262385620340, 37590614510102111241
Offset: 0
-
f:= proc(n) option remember;
- n*procname(n-1)+n^5
end proc:
f(0):= 0:
seq(f(i),i=0..21); # Robert Israel, May 13 2025
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Table[-5*n + 3*n^3 + n^4 - 2*(-1)^n*n*Subfactorial[n-1], {n, 0, 20}] (* Vaclav Kotesovec, Jul 18 2025 *)
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my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=0, 5, stirling(5, k, 2)*x^k)*exp(x)/(1+x))))
Showing 1-3 of 3 results.
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