A025752 -id:A025752 - cp's OEIS frontend

A034904 Related to sept-factorial numbers A045754.

1, 28, 980, 37730, 1531838, 64337196, 2766499428, 121034349975, 5365856182225, 240390356963680, 10861273400995360, 494187939745288880, 22618601857572837200, 1040455685448350511200, 48069052667713793617440, 2229202317465227179008780, 103723472536176158740937940

Offset: 1

Wolfdieter Lang

Convolution of A034835(n-1) with A025752(n), n >= 1.

Michael De Vlieger, Table of n, a(n) for n = 1..594
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. A025752, A034835, A045754, A220086.

CoefficientList[Series[(Power[1-49x, (-7)^-1]-1)/7,{x,0,30}],x] (* Harvey P. Dale, Aug 23 2011 *)

a(n) = 7^(n-1)*A045754(n)/n!, where A045754(n) = (7*n-6)(!^7) = Product_{j=1..n} (7*j-6).
G.f.: (-1+(1-49*x)^(-1/7))/7.
D-finite with recurrence: n*a(n) + 7*(-7*n+6)*a(n-1) = 0. - R. J. Mathar, Jan 28 2020
a(n) ~ 7^(2*n-1) * n^(-6/7) / Gamma(1/7). - Amiram Eldar, Aug 18 2025

A248329 Square array read by antidiagonals downwards: super Patalan numbers of order 7.

Original entry on oeis.org

1, 7, 42, 196, 147, 1911, 6860, 2744, 4459, 89180, 264110, 72030, 62426, 156065, 4213755, 10722866, 2218524, 1310946, 1747928, 5899257, 200574738, 450360372, 75060062, 33647614, 30588740, 55059732, 234003861, 9594158301, 19365495996, 2702162232, 975780806, 672952280, 825895980, 1872030888

Offset: 0

Tom Richardson, Oct 04 2014

Generalization of super Catalan numbers, A068555, based on Patalan numbers of order 7, A025752.

			T(0..4,0..4) is
  1           7          196        6860       264110
  42          147        2744       72030      2218524
  1911        4459       62426      1310946    33647614
  89180       156065     1747928    30588740   672952280
  4213755     5899257    55059732   825895980  15898497615

Thomas M. Richardson, The Super Patalan Numbers, arXiv:1410.5880 [math.CO], 2014.
Thomas M. Richardson, The Super Patalan Numbers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.3.3.

Cf. A068555, A025752, A034835 (first row), A216703 (first column), A248324, A248325, A248326, A248328, A248332.

matrix(5, 5, nn, kk, n=nn-1;k=kk-1;(-1)^k*49^(n+k)*binomial(n-1/7,n+k)) \\ Michel Marcus, Oct 09 2014

T(0,0)=1, T(n,k) = T(n-1,k)*(49*n-7)/(n+k), T(n,k) = T(n,k-1)*(49*k-42)/(n+k).
G.f.: (x/(1-49*x)^(6/7)+y/(1-49*y)^(1/7))/(x+y-49*x*y).
T(n,k) = (-1)^k*49^(n+k)*binomial(n-1/7,n+k).

cp's OEIS Frontend

A034904 Related to sept-factorial numbers A045754.

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