A034904 -id:A034904 - cp's OEIS frontend

A132057 A convolution triangle of numbers obtained from A034904.

1, 28, 1, 980, 56, 1, 37730, 2744, 84, 1, 1531838, 130340, 5292, 112, 1, 64337196, 6136956, 299782, 8624, 140, 1, 2766499428, 288408120, 16120314, 568008, 12740, 168, 1, 121034349975, 13561837212, 841627332, 34401528, 956970, 17640, 196, 1

Offset: 1

Wolfdieter Lang Sep 14 2007

a(n,1) = A034904(n). a(n,m)=: s2(8; n,m), a member of a sequence of unsigned triangles including s2(2; n,m)=A007318(n-1,m-1) (Pascal's triangle). s2(3;n,m)= A035324(n,m), s2(4; n,m)= A035529(n,m), s2(5; n,m)= A048882(n,m), s2(6; n,m)= A049375; s2(7; n,m)=A092083.

			{1}; {28,1}; {980,56,1}; (37730,2744,84,1);...

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
W. Lang, First 10 rows.

Cf. A132058 (row sums), A132059 (negative of alternating row sums).

a[n_, m_] := a[n, m] = 7*(7*(n-1) + m)*a[n-1, m]/n + m*a[n-1, m-1]/n;
a[n_, m_] /; n < m = 0; a[_, 0] = 0; a[1, 1] = 1;
Flatten[Table[a[n, m], {n, 1, 8}, {m, 1, n}]][[1 ;; 36]]
(* Jean-François Alcover, Jun 17 2011 *)

a(n, m) = 7*(7*(n-1)+m)*a(n-1, m)/n + m*a(n-1, m-1)/n, n >= m >= 1; a(n, m) := 0, n

G.f. for m-th column: ((-1+(1-49*x)^(-1/7))/7)^m.

A034996 Related to octo-factorial numbers A045755.

Original entry on oeis.org

1, 36, 1632, 81600, 4308480, 235530240, 13189693440, 751812526080, 43438057062400, 2536782532444160, 149439552820346880, 8866746800673914880, 529276578255612149760, 31756594695336728985600, 1913864106972293533532160, 115788778471823758778695680, 7029059963701301121153761280

Offset: 1

Wolfdieter Lang

Convolution of A034977(n-1) with A025753(n), n >= 1.

Michael De Vlieger, Table of n, a(n) for n = 1..555
Elżbieta Liszewska and Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.
Index entries for sequences related to factorial numbers.

Cf. A045755, A034977, A025753, A034904, A203142.

Rest@ CoefficientList[Series[(-1 + (1 - 64*x)^(-1/8))/8, {x, 0, 14}], x] (* Michael De Vlieger, Oct 13 2019 *)

a(n) = 8^(n-1)*A045755(n)/n!, where A045755(n) = (8*n-7)!^8 = Product_{j=1..n} (8*j-7).
G.f.: (-1+(1-64*x)^(-1/8))/8.
D-finite with recurrence: n*a(n) + 8*(-8*n+7)*a(n-1) = 0. - R. J. Mathar, Jan 28 2020
a(n) ~ 8^(2*n-1) * n^(-7/8) / Gamma(1/8). - Amiram Eldar, Aug 18 2025

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cp's OEIS Frontend

A132057 A convolution triangle of numbers obtained from A034904.

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