A045624 -id:A045624 - cp's OEIS frontend

A030526 A convolution triangle of numbers obtained from A036070.

1, 10, 1, 80, 20, 1, 560, 260, 30, 1, 3584, 2720, 540, 40, 1, 21504, 24768, 7480, 920, 50, 1, 122880, 204288, 87552, 15840, 1400, 60, 1, 675840, 1562880, 908352, 225936, 28800, 1980, 70, 1, 3604480, 11264000, 8595200, 2813696, 483920, 47360, 2660, 80

Offset: 1

Wolfdieter Lang

a(n,m) := s1p(5; n,m), a member of a sequence of unsigned triangles including s1p(2; n,m)= A007318(n-1,m-1) (Pascal's triangle). Signed version: (-1)^(n-m)*a(n,m) := s1(5; n,m).

			1;
10,1;
80,20,1;
560,260,30,1;
3584,2720,540,40,1;
...

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

a(n, 1)= A036070(n-1). Row sums = A045624(n).

a(n, m) = 4*(4*m+n-1)*a(n-1, m)/n + m*a(n-1, m-1)/n, n >= m >= 1; a(n, m) := 0, n

A046757 Triangle of coefficients of certain polynomials (exponents in decreasing order).

Original entry on oeis.org

1, 2, 1, 5, 5, 1, 30, 30, 10, 1, 272, 272, 102, 17, 1, 3250, 3250, 1300, 260, 26, 1, 47952, 47952, 19980, 4440, 555, 37, 1, 840350, 840350, 360150, 85750, 12250, 1050, 50, 1, 17039360, 17039360, 7454720, 1863680, 291200, 29120, 1820, 65, 1, 392203458

Offset: 0

Wolfdieter Lang

			Triangle begins:
  {1};
  {2,1};
  {5,5,1};
  {30,30,10,1};
  {272,272,102,17,1};
  ....
E.g. third row {5,5,1} corresponds to polynomial q(3,x)= 5*x^2+5*x+1.

x*p(k-1, -x)/q(k, -x), with the row polynomials p(n, x) from triangle A033842(n, m) is for k=1..5 g.f. for A000079 (powers of two), A039717, A043553, A045624, A046088, respectively.

a(n, n) = 1, a(n, m) = (1+n^2)*binomial(n, m)*n^(n-m-2), n>m >= 0, else 0.

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cp's OEIS Frontend

A030526 A convolution triangle of numbers obtained from A036070.

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